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Lyapunov functions and finite-time stabilization in optimal time for homogeneous linear and quasilinear hyperbolic systems Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2022-04-19 Jean-Michel Coron,Hoai-Minh Nguyen
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Long-time asymptotics of solutions to the Keller–Rubinow model for Liesegang rings in the fast reaction limit Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2022-04-06 Zymantas Darbenas,Rein van der Hout,Marcel Oliver
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Two-dimensional gravity waves at low regularity II: Global solutions Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2022-04-06 Albert Ai,Mihaela Ifrim,Daniel Tataru
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Asymptotic analysis of the linearized Boltzmann collision operator from angular cutoff to non-cutoff Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2022-03-29 Ling-Bing He,Yu-Long Zhou
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Traveling wave solutions to the Allen–Cahn equation Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2022-03-11 Chao-Nien Chen,Vittorio Coti Zelati
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Construction of maximal functions associated with skewed cylinders generated by incompressible flows and applications Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2022-03-11 Jincheng Yang
We construct a maximal function associated with a family of skewed cylinders. These cylinders, which are defined as tubular neighborhoods of trajectories of a mollified flow, appear in the study of fluid equations such as the Navier-Stokes equations and the Euler equations. We define a maximal function subordinate to these cylinders, and show it is of weak type $(1, 1)$ and strong type $(p, p)$ by
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Traveling waves for a nonlocal KPP equation and mean-field game models of knowledge diffusion Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2022-03-11 Alessio Porretta,Luca Rossi
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Analytic maps of parabolic and elliptic type with trivial centralisers Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2022-03-11 Artur Avila,Davoud Cheraghi,Alexander Eliad
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Optimal decay rate for higher-order derivatives of the solution to the Lagrangian-averaged Navier–Stokes-$\alpha$ equation in $\mathbb{R}^3$ Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2022-03-11 Jincheng Gao,Zeyu Lyu,Zheng-an Yao
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A fast regularisation of a Newtonian vortex equation Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2022-03-11 José A. Carrillo,David Gómez-Castro,Juan Luis Vázquez
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Anisotropy and stratification effects in the dynamics of fast rotating compressible fluids Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2022-03-11 Edoardo Bocchi,Francesco Fanelli,Christophe Prange
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Reaction–diffusion equations in the half-space Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2022-03-11 Henri Berestycki,Cole Graham
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Effective viscosity of random suspensions without uniform separation Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2022-03-11 Mitia Duerinckx
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Unbounded growth of the energy density associated to the Schrödinger map and the binormal flow Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2022-03-11 Valeria Banica,Luis Vega
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A Bernstein-type theorem for minimal graphs over convex domains Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2022-03-11 Nick Edelen,Zhehui Wang
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Freely floating objects on a fluid governed by the Boussinesq equations Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2022-03-11 Geoffrey Beck,David Lannes
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Regularity of the optimal sets for the second Dirichlet eigenvalue Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2022-03-09 Dario Mazzoleni,Baptiste Trey,Bozhidar Velichkov
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Optimal linearization of vector fields on the torus in non-analytic Gevrey classes Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2022-03-09 Abed Bounemoura
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Global well-posedness of a binary–ternary Boltzmann equation Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2022-02-25 Ioakeim Ampatzoglou,Irene M. Gamba,Nataša Pavlović,Maja Tasković
In this paper we prove global well-posedness for small initial data for the binary-ternary Boltzmann equation. The binary-ternary Boltzmann equation provides a correction term to the classical Boltzmann equation, taking into account both binary and ternary interactions of particles, and could possibly serve as a more accurate description model for denser gases in non-equilibrium. To prove global well-posedness
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Positive Lyapunov exponent for random perturbations of predominantly expanding multimodal circle maps Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2022-02-25 Alex Blumenthal,Yun Yang
We study the effects of IID random perturbations of amplitude $\epsilon > 0$ on the asymptotic dynamics of one-parameter families $\{f_a : S^1 \to S^1, a \in [0,1]\}$ of smooth multimodal maps which "predominantly expanding", i.e., $|f'_a| \gg 1$ away from small neighborhoods of the critical set $\{ f'_a = 0 \}$. We obtain, for any $\epsilon > 0$, a \emph{checkable, finite-time} criterion on the parameter
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On threshold solutions of the equivariant Chern–Simons–Schrödinger equation Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2022-02-25 Zexing Li,Baoping Liu
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Long-time dynamics of a hinged-free plate driven by a nonconservative force Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2022-02-25 Justin Webster,Denis Bonheure,Filippo Gazzola,Irena Lasiecka
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Stability threshold of two-dimensional Couette flow in Sobolev spaces Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2022-02-16 Nader Masmoudi,Weiren Zhao
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Long-time behavior of scalar conservation laws with critical dissipation Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2022-02-09 Dallas Albritton,Rajendra Beekie
The critical Burgers equation $\partial_t u + u \partial_x u + \Lambda u = 0$ is a toy model for the competition between transport and diffusion with regard to shock formation in fluids. It is well known that smooth initial data does not generate shocks in finite time. Less is known about the long-time behavior for `shock-like' initial data: $u_0 \to \pm a$ as $x \to \mp \infty$. We describe this long-time
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Vanishing viscosity limit of the three-dimensional barotropic compressible Navier–Stokes equations with degenerate viscosities and far-field vacuum Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2022-02-09 Geng Chen,Gui-Qiang G. Chen,Shengguo Zhu
We are concerned with the inviscid limit of the Navier-Stokes equations to the Euler equations for barotropic compressible fluids in $\mathbb{R}^3$. When the viscosity coefficients obey a lower power-law of the density (i.e., $\rho^\delta$ with $0<\delta<1$), we identify a quasi-symmetric hyperbolic--singular elliptic coupled structure of the Navier-Stokes equations to control the behavior of the velocity
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Classical and weak solutions to local first-order mean field games through elliptic regularity Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2022-02-09 Sebastian Muñoz
We study the regularity and well-posedness of the local, first-order forward-backward Mean Field Games system, assuming a polynomially growing cost function and a Hamiltonian of quadratic growth. We consider systems and terminal data which are strictly monotone in the density and study two different regimes depending on whether there exists a lower bound for the running cost function. The work relies
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On the correction to Einstein’s formula for the effective viscosity Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2022-02-09 David Gérard-Varet,Amina Mecherbet
This paper is a follow-up of article [6], on the derivation of accurate effective models for viscous dilute suspensions. The goal is to identify an effective Stokes equation providing a $o(\lambda^2)$ approximation of the exact fluid-particle system, with $\lambda$ the solid volume fraction of the particles. This means that we look for an improvement of Einstein's formula for the effective viscosity
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High degeneracy of effective Hamiltonian in two dimensions Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2022-02-09 Yifeng Yu
Consider the effective Hamiltonian $\overline H(p)$ associated with the mechanical Hamiltonian $H(p,x)={1\over 2}|p|^2+V(x)$. We prove that for generic $V$, $\overline H$ is piecewise 1d in a dense open set in two dimensions using Aubry-Mather theory.
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Global existence of weak solutions to the Navier–Stokes–Korteweg equations Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2022-02-09 Paolo Antonelli,Stefano Spirito
In this paper we consider the Navier-Stokes-Korteweg equations for a viscous compressible fluid with capillarity effects in three space dimensions. We prove global existence of finite energy weak solutions for large initial data. Contrary to previous results regarding this system, vacuum regions are allowed in the definition of weak solutions and no additional damping terms are considered. The convergence
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Refined asymptotics for the blow-up solution of the complex Ginzburg–Landau equation in the subcritical case Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2022-02-09 Giao Ky Duong,Nejla Nouaili,Hatem Zaag
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Soliton resolution for the focusing modified KdV equation Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2021-02-19 Gong Chen, Jiaqi Liu
The soliton resolution for the focusing modified Korteweg-de Vries (mKdV) equation is established for initial conditions in some weighted Sobolev spaces. Our approach is based on the nonlinear steepest descent method and its reformulation through ∂‾-derivatives. From the view of stationary points, we give precise asymptotic formulas along trajectory x=vt for any fixed v. To extend the asymptotics to
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Compactness of scalar-flat conformal metrics on low-dimensional manifolds with constant mean curvature on boundary Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2021-02-19 Seunghyeok Kim, Monica Musso, Juncheng Wei
We concern C2-compactness of the solution set of the boundary Yamabe problem on smooth compact Riemannian manifolds with boundary provided that their dimensions are 4, 5 or 6. By conducting a quantitative analysis of a linear equation associated with the problem, we prove that the trace-free second fundamental form must vanish at possible blow-up points of a sequence of blowing-up solutions. Applying
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Collapsing and the convex hull property in a soap film capillarity model Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2021-02-15 Darren King, Francesco Maggi, Salvatore Stuvard
Soap films hanging from a wire frame are studied in the framework of capillarity theory. Minimizers in the corresponding variational problem are known to consist of positive volume regions with boundaries of constant mean curvature/pressure, possibly connected by “collapsed” minimal surfaces. We prove here that collapsing only occurs if the mean curvature/pressure of the bulky regions is negative,
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Global C∞ regularity of the steady Prandtl equation with favorable pressure gradient Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2021-02-15 Yue Wang, Zhifei Zhang
In the case of favorable pressure gradient, Oleinik obtained the global-in-x solutions to the steady Prandtl equations with low regularity (see Oleinik and Samokhin [9], P.21, Theorem 2.1.1). Due to the degeneracy of the equation near the boundary, the question of higher regularity of Oleinik's solutions remains open. See the local-in-x higher regularity established by Guo and Iyer [5]. In this paper
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Full cross-diffusion limit in the stationary Shigesada-Kawasaki-Teramoto model Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2021-02-15 Kousuke Kuto
This paper studies the asymptotic behavior of coexistence steady-states of the Shigesada-Kawasaki-Teramoto model as both cross-diffusion coefficients tend to infinity at the same rate. In the case when either one of two cross-diffusion coefficients tends to infinity, Lou and Ni [18] derived a couple of limiting systems, which characterize the asymptotic behavior of coexistence steady-states. Recently
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Stability, well-posedness and regularity of the homogeneous Landau equation for hard potentials Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2021-02-15 Nicolas Fournier, Daniel Heydecker
We establish the well-posedness and some quantitative stability of the spatially homogeneous Landau equation for hard potentials, using some specific Monge-Kantorovich cost, assuming only that the initial condition is a probability measure with a finite moment of order p for some p>2. As a consequence, we extend previous regularity results and show that all non-degenerate measure-valued solutions to
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Global semiclassical limit from Hartree to Vlasov equation for concentrated initial data Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2021-02-05 Laurent Lafleche
We prove a quantitative and global in time semiclassical limit from the Hartree to the Vlasov equation in the case of a singular interaction potential in dimension d≥3, including the case of a Coulomb singularity in dimension d=3. This result holds for initial data concentrated enough in the sense that some space moments are initially sufficiently small. As an intermediate result, we also obtain quantitative
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Vanishing viscosity limit of the 3D incompressible Oldroyd-B model Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2021-02-05 Ruizhao Zi
Consider the vanishing viscosity limit of the 3D incompressible Oldroyd-B model. It is shown that this set of equations admits a unique global solution with small analytic data uniformly in the coupling parameter ω close to 1 that corresponds to the inviscid case. We justify the limit from the Oldroyd-B model to the inviscid case ω=1 for all time. Moreover, if the nonlinear term gα(τ,∇u) is ignored
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The influence of Einstein's effective viscosity on sedimentation at very small particle volume fraction Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2021-02-05 Richard M. Höfer, Richard Schubert
We investigate the sedimentation of identical inertialess spherical particles in a Stokes fluid in the limit of many small particles. It is known that the presence of the particles leads to an increase of the effective viscosity of the suspension. By Einstein's formula this effect is of the order of the particle volume fraction ϕ. The disturbance of the fluid flow responsible for this increase of viscosity
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Polyhomogénéité des métriques compatibles avec une structure de Lie à l'infini le long du flot de Ricci Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2021-02-05 Mahdi Ammar
Le long du flot de Ricci, on étudie la polyhomogénéité des métriques pour des variétés riemanniennes non-compactes ayant « une structure de Lie fibrée à l'infini », c'est-à-dire une classe de structures de Lie à l'infini qui induit dans un sens précis des structures de fibrés sur les bords d'une certaine compactification par une variété à coins. Lorsque cette compactification est une variété à bord
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The Pohozaev-Schoen identity on asymptotically Euclidean manifolds: Conservation laws and their applications Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2021-02-05 R. Avalos, A. Freitas
The aim of this paper is to present a version of the generalized Pohozaev-Schoen identity in the context of asymptotically Euclidean manifolds. Since these kind of geometric identities have proven to be a very powerful tool when analysing different geometric problems for compact manifolds, we will present a variety of applications within this new context. Among these applications, we will show some
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Stability of planar rarefaction waves under general viscosity perturbation of the isentropic Euler system Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2021-02-05 Eduard Feireisl, Antonín Novotný
We consider the vanishing viscosity limit for a model of a general non-Newtonian compressible fluid in Rd, d=2,3. We suppose that the initial data approach a profile determined by the Riemann data generating a planar rarefaction wave for the isentropic Euler system. Under these circumstances the associated sequence of dissipative solutions approaches the corresponding rarefaction wave strongly in the
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Non-existence of patterns and gradient estimates in semilinear elliptic equations with Neumann boundary conditions Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2021-02-05 Samuel Nordmann
We call pattern any non-constant solution of a semilinear elliptic equation with Neumann boundary conditions. A classical theorem of Casten, Holland [20] and Matano [50] states that stable patterns do not exist in convex domains. In this article, we show that the assumptions of convexity of the domain and stability of the pattern in this theorem can be relaxed in several directions. In particular,
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A normalized solitary wave solution of the Maxwell-Dirac equations Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2021-01-12 Margherita Nolasco
We prove the existence of a L2-normalized solitary wave solution for the Maxwell-Dirac equations in (3+1)-Minkowski space. In addition, for the Coulomb-Dirac model, describing fermions with attractive Coulomb interactions in the mean-field limit, we prove the existence of the (positive) energy minimizer.
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The lifespan of classical solutions for the inviscid Surface Quasi-geostrophic equation Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2021-01-04 Ángel Castro, Diego Córdoba, Fan Zheng
We consider classical solutions of the inviscid Surface Quasi-geostrophic equation that are a small perturbation ϵ from a radial stationary solution θ=|x|. We use a modified energy method to prove the existence time of classical solutions from 1ϵ to a time scale of 1ϵ4. Moreover, by perturbing in a suitable direction we construct global smooth solutions, via bifurcation, that rotate uniformly in time
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Non dispersive solutions of the generalized Korteweg-de Vries equations are typically multi-solitons Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2021-01-04 Xavier Friederich
We consider solutions of the generalized Korteweg-de Vries equations (gKdV) which are non dispersive in some sense and which remain close to multi-solitons. We show that these solutions are necessarily pure multi-solitons. For the Korteweg-de Vries equation (KdV) and the modified Korteweg-de Vries equation (mKdV) in particular, we obtain a characterization of multi-solitons and multi-breathers in terms
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On the controllability and stabilization of the Benjamin equation on a periodic domain Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2020-12-30 M. Panthee, F. Vielma Leal
The aim of this paper is to study the controllability and stabilization for the Benjamin equation on a periodic domain T. We show that the Benjamin equation is globally exactly controllable and globally exponentially stabilizable in Hps(T), with s≥0. The global exponential stabilizability corresponding to a natural feedback law is first established with the aid of certain properties of solution, viz
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Multiphase free discontinuity problems: Monotonicity formula and regularity results Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2020-12-29 Dorin Bucur, Ilaria Fragalà, Alessandro Giacomini
The purpose of this paper is to analyze regularity properties of local solutions to free discontinuity problems characterized by the presence of multiple phases. The key feature of the problem is related to the way in which two neighboring phases interact: the contact is penalized at jump points, while no cost is assigned to no-jump interfaces which may occur at the zero level of the corresponding
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On unique continuation principles for some elliptic systems Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2020-12-28 Ederson Moreira dos Santos, Gabrielle Nornberg, Nicola Soave
In this paper we prove unique continuation principles for some systems of elliptic partial differential equations satisfying a suitable superlinearity condition. As an application, we obtain nonexistence of nontrivial (not necessarily positive) radial solutions for the Lane-Emden system posed in a ball, in the critical and supercritical regimes. Some of our results also apply to general fully nonlinear
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Local limit of nonlocal traffic models: Convergence results and total variation blow-up Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2020-12-28 Maria Colombo, Gianluca Crippa, Elio Marconi, Laura V. Spinolo
Consider a nonlocal conservation law where the flux function depends on the convolution of the solution with a given kernel. In the singular local limit obtained by letting the convolution kernel converge to the Dirac delta one formally recovers a conservation law. However, recent counter-examples show that in general the solutions of the nonlocal equations do not converge to a solution of the conservation
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Long time confinement of vorticity around a stable stationary point vortex in a bounded planar domain Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2020-12-01 Martin Donati, Dragoș Iftimie
In this paper we consider the incompressible Euler equation in a simply-connected bounded planar domain. We study the confinement of the vorticity around a stationary point vortex. We show that the power law confinement around the center of the unit disk obtained in [2] remains true in the case of a stationary point vortex in a simply-connected bounded domain. The domain and the stationary point vortex
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Conditional stability of multi-solitons for the 1D NLKG equation with double power nonlinearity Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2020-12-01 Xu Yuan
We consider the one-dimensional nonlinear Klein-Gordon equation with a double power focusing-defocusing nonlinearity∂t2u−∂x2u+u−|u|p−1u+|u|q−1u=0,on[0,∞)×R, where 1
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Edge-localized states on quantum graphs in the limit of large mass Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2020-12-01 Gregory Berkolaiko, Jeremy L. Marzuola, Dmitry E. Pelinovsky
We construct and quantify asymptotically in the limit of large mass a variety of edge-localized stationary states of the focusing nonlinear Schrödinger equation on a quantum graph. The method is applicable to general bounded and unbounded graphs. The solutions are constructed by matching a localized large amplitude elliptic function on a single edge with an exponentially smaller remainder on the rest
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Phase transitions on the Markov and Lagrange dynamical spectra Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2020-12-01 Davi Lima, Carlos Gustavo Moreira
The Markov and Lagrange dynamical spectra were introduced by Moreira and share several geometric and topological aspects with the classical ones. However, some features of generic dynamical spectra associated to hyperbolic sets can be proved in the dynamical case and we do not know if they are true in classical case. They can be a good source of natural conjectures about the classical spectra: it is
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Stability of equilibria uniformly in the inviscid limit for the Navier-Stokes-Poisson system Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2020-11-30 Frédéric Rousset, Changzhen Sun
We prove a stability result of constant equilibria for the three dimensional Navier-Stokes-Poisson system uniform in the inviscid limit. We allow the initial density to be close to a constant and the potential part of the initial velocity to be small independently of the rescaled viscosity parameter ε while the incompressible part of the initial velocity is assumed to be small compared to ε. We then
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On critical points of the relative fractional perimeter Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2020-11-30 Andrea Malchiodi, Matteo Novaga, Dayana Pagliardini
We study the localization of sets with constant nonlocal mean curvature and prescribed small volume in a bounded open set, proving that they are sufficiently close to critical points of a suitable nonlocal potential. We then consider the fractional perimeter in half-spaces. We prove existence of minimizers under fixed volume constraint, and we show some properties such as smoothness and rotational
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Regularity of optimal sets for some functional involving eigenvalues of an operator in divergence form Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2020-11-27 Baptiste Trey
In this paper we consider minimizers of the functionalmin{λ1(Ω)+⋯+λk(Ω)+Λ|Ω|,:Ω⊂D open} where D⊂Rd is a bounded open set and where 0<λ1(Ω)≤⋯≤λk(Ω) are the first k eigenvalues on Ω of an operator in divergence form with Dirichlet boundary condition and with Hölder continuous coefficients. We prove that the optimal sets Ω⁎ have finite perimeter and that their free boundary ∂Ω⁎∩D is composed of a regular
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Critical chirality in elliptic systems Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2020-11-27 Francesca Da Lio, Tristan Rivière
We establish the regularity in 2 dimension of L2 solutions to critical elliptic systems in divergence form involving chirality operators of finite W1,2-energy.
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Point interactions for 3D sub-Laplacians Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2020-11-27 Riccardo Adami, Ugo Boscain, Valentina Franceschi, Dario Prandi
In this paper we show that, for a sub-Laplacian Δ on a 3-dimensional manifold M, no point interaction centered at a point q0∈M exists. When M is complete w.r.t. the associated sub-Riemannian structure, this means that Δ acting on C0∞(M∖{q0}) is essentially self-adjoint in L2(M). A particular example is the standard sub-Laplacian on the Heisenberg group. This is in stark contrast with what happens in
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Gevrey regularity for the Vlasov-Poisson system Ann. I. H. Poincaré – AN (IF 1.9) Pub Date : 2020-11-13 Renato Velozo Ruiz
We prove propagation of 1s-Gevrey regularity (s∈(0,1]) for the Vlasov-Poisson system on Td×Rd using a Fourier space method in analogy to the results proved for the 2D-Euler system in [20] and [23]. More precisely, we give quantitative estimates for the growth of the 1s-Gevrey norm and decay of the regularity radius for the solution of the system in terms of the force field and the volume of the support