SIAM Journal on Mathematical Analysis, Volume 53, Issue 4, Page 4142-4177, January 2021. In this paper, we consider a two-dimensional nonresistive magnetohydrodynamic model, taking the fluctuation of absolute temperature into account. Combining the method of weak convergence developed by Lions [Mathematical Topics in Fluid Mechanics: Volume 2: Compressible Models, Clarendon Press, Oxford, UK, 1998]

SIAM Journal on Mathematical Analysis, Volume 53, Issue 4, Page 4118-4141, January 2021. We establish the future stability of nonlinear perturbations of a class of homogeneous solutions to the relativistic Euler equations with a linear equation of state $p=K\rho$ on exponentially expanding Friedmann--Lemaître--Robertson--Walker spacetimes for the equation of state parameter values $1/3 < K < 1/2$.

SIAM Journal on Mathematical Analysis, Volume 53, Issue 4, Page 4096-4117, January 2021. For $\partial\Omega$ the boundary of a bounded and connected strongly Lipschitz domain in $\mathbb{R}^{d}$ with $d\geq3$, we prove that any field $f\in L^{2}(\partial\Omega ; \mathbb{R}^{d})$ decomposes, in a unique way, as the sum of three invisible vector fields---fields whose magnetic potential vanishes in one

SIAM Journal on Mathematical Analysis, Volume 53, Issue 4, Page 4068-4095, January 2021. We study the time-harmonic Galbrun equation describing the propagation of sound in the presence of a steady background flow. With additional rotational and gravitational terms these equations are also fundamental in helio- and asteroseismology as a model for stellar oscillations. For a simple damping model we prove

SIAM Journal on Mathematical Analysis, Volume 53, Issue 4, Page 4031-4067, January 2021. We consider state-dependent delay equations (SDDEs) obtained by adding delays to a planar ODE with a limit cycle. Situations of this type appear in models of several physical processes, where small delay effects are added. Even if the delays are small, they are very singular perturbations since the natural phase

SIAM Journal on Mathematical Analysis, Volume 53, Issue 4, Page 3985-4030, January 2021. We prove the existence of large-data global-in-time weak solutions to an evolutionary PDE system describing flows of incompressible heat-conducting viscoelastic rate-type fluids with stress-diffusion, subject to a stick-slip boundary condition for the velocity and a homogeneous Neumann boundary condition for the

SIAM Journal on Mathematical Analysis, Volume 53, Issue 4, Page 3958-3984, January 2021. In this paper, we consider a fluid-particle system which describes the evolution of a two-phase flow. The system consists of the compressible Euler equations for the fluid (fluid phase) coupled with the Vlasov equation for the particles (disperse phase) through the drag force. We obtain a global bounded weak entropy

SIAM Journal on Mathematical Analysis, Volume 53, Issue 4, Page 3912-3957, January 2021. Since the breakthrough in rough paths theory for stochastic ordinary differential equations, there has been a strong interest in investigating the rough differential equation (RDE) approach and its numerous applications. Rough path techniques can stay closer to deterministic analytical methods and have the potential

SIAM Journal on Mathematical Analysis, Volume 53, Issue 4, Page 3888-3911, January 2021. We study boundary integral formulations for an interior/exterior initial boundary value problem arising from the thermo-elasto-dynamic equations in a homogeneous and isotropic domain. The time dependence is handled, based on Lubich's approach, through a passage to the Laplace domain. We focus on the cases where

SIAM Journal on Mathematical Analysis, Volume 53, Issue 4, Page 3856-3887, January 2021. In this paper, we study the energy balance for a class of solutions of the Navier--Stokes equations with external forces in dimensions three and above. The solution and force are smooth on $(0,T)$ and the total dissipation and work of the force are both finite. We show that a possible failure of the energy balance

SIAM Journal on Mathematical Analysis, Volume 53, Issue 4, Page 3838-3855, January 2021. We are concerned with the decay of long time solutions of the IVP associated to the Schrödinger--Korteweg--de Vries system. We use recent techniques in order to show that solutions of this system decay to zero in the energy space. The result is independent of the integrability of the equations involved, and it

SIAM Journal on Mathematical Analysis, Volume 53, Issue 4, Page 3801-3837, January 2021. We consider several intriguingly connected topics in the theory of wave propagation: geometrical characterizations of radiationless sources, nonradiating incident waves, interior transmission eigenfunctions, and their applications to inverse scattering. Our major novel discovery is a localization and geometrization

SIAM Journal on Mathematical Analysis, Volume 53, Issue 4, Page 3772-3800, January 2021. In order to improve the frequency dispersion effects of irrotational shallow water models in coastal oceanography, several full dispersion versions of classical models have been formally derived in the literature. The idea, coming from G. Whitham in [Proc. A, 299 (1967), pp.6--25] was to modify them so that their

SIAM Journal on Mathematical Analysis, Volume 53, Issue 4, Page 3759-3771, January 2021. The Lamé system is a classical model for isotropic elasticity and has important applications in seismology. In the present paper, we study the longtime dynamics of weakly damped Lamé systems that exhibit interior delay effects on the velocity. The main result establishes, under nonlinear forces of critical growth

SIAM Journal on Mathematical Analysis, Volume 53, Issue 4, Page 3717-3758, January 2021. For a slow-fast system of the form $\dot{p}=\epsilon f(p,z,\epsilon)+h(p,z,\epsilon)$, $\dot{z}=g(p,z,\epsilon)$ for $(p,z)\in \mathbb R^n\times \mathbb R^m$, we consider the scenario that the system has invariant sets $M_i=\{(p,z): z=z_i\}$, $1\le i\le N$, linked by a singular closed orbit formed by trajectories

SIAM Journal on Mathematical Analysis, Volume 53, Issue 3, Page 3681-3715, January 2021. We prove a Wong--Zakai theorem for the defocusing stochastic mass-critical nonlinear Schrödinger equation on $\mathbb{R}$. The main ingredients are careful mixtures of bootstrapping arguments at both deterministic and stochastic levels. Several subtleties arising from the proof mark the difference between the dispersive

SIAM Journal on Mathematical Analysis, Volume 53, Issue 3, Page 3661-3680, January 2021. For the solution of the scattering problem for time-harmonic electromagnetic waves with boundary conditions for the normal components of both the electric and the magnetic field, an integral equation method proposed by Gülzow in 1988 is reconsidered. It is made more concise, made symmetric with respect to the electric

SIAM Journal on Mathematical Analysis, Volume 53, Issue 3, Page 3644-3660, January 2021. In this article, we study long time dynamics for defocusing cubic nonlinear Schrödinger equations (NLS) on three dimensional product space. First, we apply the decoupling method in Bourgain and Demeter [Ann. of Math. (2), 182 (2015), pp. 351--389] to establish a bilinear Strichartz estimate. Moreover, we prove

SIAM Journal on Mathematical Analysis, Volume 53, Issue 3, Page 3602-3643, January 2021. We are interested in the spectral properties of the magnetic Schrödinger operator $H_\varepsilon$ in a domain $\Omega \subset \mathbb{R}^2$ with compact boundary and with magnetic field of intensity $\varepsilon^{-2}$. We impose Dirichlet boundary conditions on $\partial\Omega$. Our main focus is the existence

SIAM Journal on Mathematical Analysis, Volume 53, Issue 3, Page 3577-3601, January 2021. We investigate the existence and uniqueness of solutions to second-order elliptic boundary value problems containing a power nonlinearity applied to a fractional Laplacian. We detect the critical power separating the existence from the nonexistence regimes. For the existence results, we make use of a particular

SIAM Journal on Mathematical Analysis, Volume 53, Issue 3, Page 3520-3576, January 2021. Motivated by pulse-replication phenomena observed in the FitzHugh--Nagumo equation, we investigate traveling pulses whose slow/fast profiles exhibit canard-like transitions. We show that the spectra of the PDE linearization about such pulses may contain many point eigenvalues that accumulate onto a union of curves

SIAM Journal on Mathematical Analysis, Volume 53, Issue 3, Page 3493-3519, January 2021. We consider two nonlocal variational models arising in physical contexts. The first is the Thomas--Fermi--Dirac--von Weizsäcker (TFDW) model, introduced in the study of ionization of atoms and molecules, and the second is the liquid drop model with external potential, proposed by Gamow in the context of nuclear

SIAM Journal on Mathematical Analysis, Volume 53, Issue 3, Page 3420-3492, January 2021. A rate-independent model coupling small-strain associative elasto-plasticity and damage is studied via a vanishing-viscosity analysis with respect to all the variables describing the system. This extends the analysis performed for the same system in [V. Crismale and G. Lazzaroni, Calc. Var. Partial Differential

SIAM Journal on Mathematical Analysis, Volume 53, Issue 3, Page 3385-3419, January 2021. We study a chemotaxis model describing the space and time evolution in a smooth and bounded domain of $\mathbb{R}^2$ of the densities $u$ and $v$ of subpopulations of moving and static individuals of some species and the concentration $w$ of a chemoattractant. We prove that, in an appropriate functional setting

SIAM Journal on Mathematical Analysis, Volume 53, Issue 3, Page 3366-3384, January 2021. We prove a continuation criterion for incompressible liquids with free surface boundary when the liquid occupies a bounded region. We combine the energy estimates of Christodoulou and Lindblad [Comm. Pure Appl. Math., 53 (2000), pp. 1536--1602] with an analogue of the estimate due to Beale, Kato, and Majda [Comm

SIAM Journal on Mathematical Analysis, Volume 53, Issue 3, Page 3338-3365, January 2021. In this paper we study a gradient flow generated by the Landau--de Gennes free energy that describes nematic liquid crystal configurations in the space of $Q$-tensors. This free energy density functional is composed of three quadratic terms as the elastic energy density part, and a singular potential in the bulk

SIAM Journal on Mathematical Analysis, Volume 53, Issue 3, Page 3306-3337, January 2021. In this paper, inspired by the seminal work by Caffarelli, Kohn, and Nirenberg [Comm. Pure Appl. Math., 35 (1982), pp. 771--831] on the incompressible Navier--Stokes equation, we establish the existence of a suitable weak solution to the Navier--Stokes--Planck--Nernst--Poisson equation in dimension three, which

SIAM Journal on Mathematical Analysis, Volume 53, Issue 3, Page 3265-3305, January 2021. In this paper, we study the low Mach and Froude number limit for the all-time classical solution of a fluid-vacuum free boundary problem of one-dimensional compressible Navier--Stokes equations. No smallness of initial data for the existence of all-time solutions is supposed. The uniform estimates of solutions

SIAM Journal on Mathematical Analysis, Volume 53, Issue 3, Page 3236-3264, January 2021. We establish the well-posedness of the MHD boundary layer system in Gevrey function space without any structural assumption. Compared to the classical Prandtl equation, the loss of tangential derivative comes from both the velocity and magnetic fields that are coupled with each other. By observing a new type of

SIAM Journal on Mathematical Analysis, Volume 53, Issue 3, Page 3188-3235, January 2021. We present global-in-time existence and uniqueness of strong solutions around a phase-homogeneous solution, and its large-time behavior for the Kuramoto--Sakaguchi equation with inertia. Our governing equation describes the evolution of the probability density function for a large ensemble of Kuramoto oscillators

SIAM Journal on Mathematical Analysis, Volume 53, Issue 3, Page 3158-3187, January 2021. This paper provides an extension to fractional order Sobolev spaces of the classical result of Murat and Brezis which states that the cone of positive elements in $H^{-1}(\Omega)$ compactly embeds in $W^{-1,q}(\Omega)$ for every $q < 2$ and for any open and bounded set $\Omega$ with Lipschitz boundary. In particular

SIAM Journal on Mathematical Analysis, Volume 53, Issue 3, Page 3123-3157, January 2021. We consider a magnetic effect on hydrodynamic flows of nematic liquid crystals with unequal elastic constants in dimension two. Under a planar ansatz for the director field and velocity, we derive a reduced Ericksen--Leslie system which consists of a quasilinear parabolic equation and a Navier--Stokes equation

SIAM Journal on Mathematical Analysis, Volume 53, Issue 3, Page 3098-3122, January 2021. We prove norm-resolvent and spectral convergence in $L^2$ of solutions to the Neumann Poisson problem $-\Delta u_\varepsilon = f$ on a domain $\Omega_\varepsilon$ perforated by Dirichlet holes and shrinking to a 1-dimensional interval. The limit $u$ satisfies an equation of the type $-u''+\mu u = f$ on the interval

SIAM Journal on Mathematical Analysis, Volume 53, Issue 3, Page 3072-3097, January 2021. Most technologically useful materials are polycrystalline microstructures composed of myriad small monocrystalline grains separated by grain boundaries. The energetics and connectivities of grain boundaries play a crucial role in defining the main characteristics of materials across a wide range of scales. In this

SIAM Journal on Mathematical Analysis, Volume 53, Issue 3, Page 3040-3071, January 2021. We study the global wellposedness of pressureless Eulerian dynamics in multidimensions, with radially symmetric data. Compared with the one-dimensional system, a major difference in multidimensional Eulerian dynamics is the presence of the spectral gap, which is difficult to control in general. We propose a new

SIAM Journal on Mathematical Analysis, Volume 53, Issue 3, Page 3016-3039, January 2021. Peaked periodic waves in the Camassa--Holm equation are revisited. Linearized evolution equations are derived for perturbations to the peaked periodic waves, and linearized instability is proven in both $H^1$ and $W^{1,\infty}$ norms. Dynamics of perturbations in $H^1$ is related to the existence of two conserved

SIAM Journal on Mathematical Analysis, Volume 53, Issue 3, Page 3002-3015, January 2021. If the integrals of a one-form over all lines meeting a small open set vanish and the form is closed in this set, then the one-form is exact in the whole Euclidean space. We obtain a unique continuation result for the normal operator of the x-ray transform of one-forms, and this leads to one of our two proofs of

SIAM Journal on Mathematical Analysis, Volume 53, Issue 3, Page 2957-3001, January 2021. This paper studies homogenization of symmetric nonlocal Dirichlet forms with stable-like jumping kernels in a one-parameter stationary ergodic environment. Under suitable conditions, we establish results of homogenization and identify the limiting effective Dirichlet forms explicitly. The coefficients in the jumping

SIAM Journal on Mathematical Analysis, Volume 53, Issue 3, Page 2925-2956, January 2021. In this paper, we proposed a coupled Patlak--Keller--Segel--Navier--Stokes system, which has dissipative free energy. On the plane $\mathbb{R}^2$, if the total mass of the cells is strictly less than $8\pi$, classical solutions exist for any finite time, and their $H^s$-Sobolev norms are almost uniformly bounded

SIAM Journal on Mathematical Analysis, Volume 53, Issue 3, Page 2890-2924, January 2021. We derive high order homogenized models for the incompressible Stokes system in a cubic domain filled with periodic obstacles. These models have the potential to unify the three classical limit problems (namely the “unchanged” Stokes system, the Brinkman model, and Darcy's law) corresponding to various asymptotic

SIAM Journal on Mathematical Analysis, Volume 53, Issue 3, Page 2863-2889, January 2021. We propose and analyze variational source conditions (VSC) for the Tikhonov regularization method with $L^p$-penalties applied to an ill-posed operator equation in a Banach space. Our analysis is built on the celebrated Littlewood--Paley theory and the concept of (Rademacher) R-boundedness. With these two analytical

SIAM Journal on Mathematical Analysis, Volume 53, Issue 3, Page 2811-2862, January 2021. We are concerned with the structural stability of conical shocks in the three-dimensional steady supersonic flows past Lipschitz perturbed cones whose vertex angles are less than the critical angle. The flows under consideration are governed by the steady isothermal Euler equations for potential flow with axisymmetry

SIAM Journal on Mathematical Analysis, Volume 53, Issue 3, Page 2776-2810, January 2021. In this paper, we are concerned with an epidemic reaction-diffusion system with nonlinear incidence mechanism of the form $S^qI^p\,(p,\,q>0)$. The coefficients of the system are spatially heterogeneous and time dependent (particularly time periodic). We first establish the $L^\infty$-bounds of the solutions of

SIAM Journal on Mathematical Analysis, Volume 53, Issue 3, Page 2746-2775, January 2021. This article addresses the local boundedness and Hölder continuity of weak solutions to kinetic Fokker--Planck equations with general transport operators and rough coefficients. These results are due to the mixing effect of diffusion and transport. Although the equation is parabolic only in the velocity variable

SIAM Journal on Mathematical Analysis, Volume 53, Issue 3, Page 2718-2745, January 2021. In this paper, we study the homogenization of a coupled diffusion-convection system. We consider a highly heterogeneous diffusion-convection equation in space, coupled with a stochastic differential equation with highly heterogeneous temporal scales that accounts for media change. Our main result consists of deriving

SIAM Journal on Mathematical Analysis, Volume 53, Issue 3, Page 2691-2717, January 2021. We consider the time-harmonic Maxwell's equations with physical parameters, namely, the electric permittivity and the magnetic permeability, that are complex, possibly non-Hermitian, tensor fields. Both tensor fields verify a general ellipticity condition. In this work, the well-posedness of formulations for the

SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 2660-2689, January 2021. We deal with an inverse elastic scattering problem for the shape determination of a rigid scatterer in the time-harmonic regime. We prove a local stability estimate of $log\,log$ type for the identification of a scatterer by a single far-field measurement. The needed a priori condition on the closeness of the scatterers

SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 2631-2659, January 2021. We study a Paveri-Fontana type model, which describes the evolution of the mesoscopic distribution of vehicles through a combined effect of adjustment of the velocity with respect to nearby vehicles, and slowing down and speeding up of the vehicles arising as a result of exchange of velocity with the vehicles on

SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 2595-2630, January 2021. We consider the three-dimensional incompressible free-boundary magnetohydrodynamics (MHD) equations in a bounded domain with surface tension on the boundary. We establish an priori estimate for solutions in the Lagrangian coordinates with $H^{3.5}$ regularity. To the best of our knowledge, this is the first result

SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 2567-2594, January 2021. We consider the motion of the interface between two inviscid, incompressible, and dielectric fluids with different densities and permittivities, in the presence of a uniform electric field acting in a direction parallel to the undisturbed configuration. The system is assumed to be irrotational except the interface

SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 2523-2566, January 2021. In a classical survey [Mathematics in Industrial Problems, Springer-Verlag, New York, 1989, Chapter 16.2], Friedman proposed an open problem on the collision of two incompressible jets emerging from two axially symmetric nozzles. In this paper, we are concerned with the mathematical theory on this collision problem

SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 2491-2522, January 2021. We rigorously show the nonequilibrium-diffusion limit of the compressible Euler-P1 approximation model arising in radiation hydrodynamics as the Mach number tends to zero when the initial data is well prepared. In particular, the effect of the large temperature variation upon the limit is taken into account. The

SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 2476-2490, January 2021. Recently, the higher order averaging method for studying periodic solutions of both Lipschitz differential equations and discontinuous piecewise smooth differential equations was developed in terms of the Brouwer degree theory. Between the Lipschitz and the discontinuous piecewise smooth differential equations

SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 2452-2475, January 2021. We show propagation of moments in velocity for the three-dimensional Vlasov--Poisson system with a uniform magnetic field $B=(0,0,\omega)$ by adapting the work of Lions and Perthame. The added magnetic field also produces singularities at times which are the multiples of the cyclotron period $t=\frac{2\pi k}{\omega}$

SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 2427-2451, January 2021. We study the problem of recovering the initial data ($f, 0$) of the standard wave equation from the Neumann trace (the normal derivative) of the solution on the boundary of convex domains in arbitrary spatial dimension. Among others, this problem is relevant for tomographic image reconstruction including photoacoustic

SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 2373-2426, January 2021. It is shown that in core-radius cutoff regularized simplified elasticity (where the elastic energy depends quadratically on the full displacement gradient rather than its symmetrized version), the force on a dislocation curve by the negative gradient of the elastic energy asymptotically approaches the mean curvature

SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 2349-2372, January 2021. We study a stationary scattering problem related to the nonlinear Helmholtz equation $ - \Delta u -k^2 u = f(x,u) \ \ \text{in $\mathbbR^N$,} $ where $N \ge 3$ and $k>0$. For a given incident free wave $\phi\in L^\infty({\mathbb{R}}^N)$, we prove the existence of complex-valued solutions of the form $u=\varphi+u_{\text{sc}}$

SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 2319-2348, January 2021. We study master equations of the form $(\partial_t+L)^su=f\ {in}~\mathbb{R}\times\Omega,$ where $L$ is a divergence form elliptic operator and $\Omega\subseteq\mathbb{R}^n$. These are nonlocal equations of order $2s$ in space and $s$ in time that take into account the values of $u$ everywhere in $\Omega$ and for

SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 2275-2318, January 2021. We propose and analyze a finite-difference discretization of the Ambrosio--Tortorelli functional. It is known that if the discretization is made with respect to an underlying periodic lattice of spacing $\delta$, the discretized functionals $\Gamma$-converge to the Mumford--Shah functional only if $\delta\ll\varepsilon$

SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 2243-2274, January 2021. In this paper, we prove the global well-posedness for the focusing, cubic nonlinear Schrödinger equation on the product space $\mathbb{R} \times \mathbb{T}^3$ with initial data below the threshold that arises from the the ground state in the Euclidean setting. The defocusing analogue was discussed and proved in