We consider the existence of global attractor for non-Newtonian fluids near the BCS-BEC crossover in this paper. By Gronwall’s inequality, interpolar inequality and the techniques for proving regularity theory in partial differential equations, etc., we establish suitable prior estimates and obtain the global attractor for non-Newtonian fluids.

We regard the Cauchy problem for a particular Whitham–Boussinesq system modelling surface waves of an inviscid incompressible fluid layer. The system can be seen as a weak nonlocal dispersive perturbation of the shallow water system. The proof of well-posedness relies on energy estimates. However, due to the symmetry lack of the nonlinear part, in order to close the a priori estimates one has to modify

We study the motion of charged particle under a natural choice of electromagnetic field in a general class of compact homogeneous spaces. As a special case we describe the motion in homogeneous Riemannian spaces (G/H,g), where g is any deformation of a normal metric along the fibers of a homogeneous fibration \(K/H\rightarrow G/H\rightarrow G/K\).

Given N absolutely continuous probabilities \(\rho _{1}, \dotsc , \rho _{N}\) over \({\mathbb {R}}^{d}\) which have Sobolev regularity, and given a transport plan P with marginals \(\rho _{1}, \dotsc , \rho _{N}\), we provide a universal technique to approximate P with Sobolev regular transport plans with the same marginals. Moreover, we prove a sharp control of the energy and some continuity properties

We study the spectrum and dynamics of a one-dimensional discrete Dirac operator in a random potential obtained by damping an i.i.d. environment with an envelope of type n−α for α > 0. We recover all the spectral regimes previously obtained for the analogue Anderson model in a random decaying potential, namely: absolutely continuous spectrum in the super-critical region \(\alpha >\frac 12\); a transition

For a system of N bosons in one space dimension with two-body δ-interactions the Hamiltonian can be defined in terms of the usual closed semi-bounded quadratic form. We approximate this Hamiltonian in norm resolvent sense by Schrödinger operators with rescaled two-body potentials, and we estimate the rate of this convergence.

We construct P(ϕ)1-processes indexed by the full time-line, separately derived from the functional integral representations of the relativistic and non-relativistic Nelson models in quantum field theory. These two cases differ essentially by sample path regularity. Associated with these processes we define a martingale which, under an appropriate scaling, allows to obtain a central limit theorem for

We analyse a Curie-Weiss model with two disjoint groups of spins with homogeneous coupling. We show that similarly to the single-group Curie-Weiss model a bivariate law of large numbers holds for the normed sums of both groups’ spin variables. We also show central limit theorem in the high temperature regime.

In this paper, by maximal regularity estimates for the Stokes equation, we establish the local existence of solutions to the three-dimensional magnetic Bénard system with Hall, ion-slip effects and zero thermal conductivity under the condition that the initial data *.

In this article, we study the mean curvature type flow of spacelike graphical hypersurfaces in Lorentzian warped product. This flow was introduced by Guan and Li in [6]. Under mild assumptions on the warping function and the Ricci curvature of the base manifold, we obtain the longtime existence and smooth convergence to an umbilic slice for this flow in Lorentzian setting. As an application of the

We study the structure of the Mather and Aubry sets for the family of Lagrangians given by the kinetic energy associated to a Riemannian metric g on a closed manifold M. In this case the Euler-Lagrange flow is the geodesic flow of (M, g). We prove that there exists a residual subset of the set of all conformal metrics to g, such that, if \( \overline g \in G\) then the corresponding geodesic flow has

We give a direct proof for the positivity of Kirillov’s character on the convolution algebra of smooth, compactly supported functions on a connected, simply connected nilpotent Lie group G. Then we use this positivity result to construct a representation of G × G and establish a G × G-equivariant isometric isomorphism between our representation and the Hilbert–Schmidt operators on the underlying representation

In this note, we initiate a study of the finite-dimensional representation theory of a class of algebras that correspond to noncommutative deformations of compact surfaces of arbitrary genus. Low dimensional representations are investigated in detail and graph representations are used in order to understand the structure of non-zero matrix elements. In particular, for arbitrary genus greater than one

In this paper, we provide a new approach to get global well-posedness for the 3D liquid crystal system with large vertical velocity in the critical L2 framework. The novelty is that there is not one additional derivative when we treat the pressure. Furthermore, our idea can be applied to get global well-posedness for the 3D damped Euler equations with large vertical velocity, while the previous ideas

Using a left multiplication defined on a right quaternionic Hilbert space, we shall demonstrate that pure squeezed states, which are obtained by the sole action of the squeeze operator on the vacuum state, can be defined with all the desired properties on a right quaternionic Hilbert space. Further, we shall also demonstrate that squeezed states, which are obtained by the action of the squeeze operator

We prove that for every semigroup of Schwarz maps on the von Neumann algebra of all bounded linear operators on a Hilbert space which has a subinvariant faithful normal state there exists an associated semigroup of contractions on the space of Hilbert-Schmidt operators of the Hilbert space. Moreover, we show that if the original semigroup is weak∗ continuous then the associated semigroup is strongly

We consider a generic system composed of a fixed number of particles distributed over a finite number of energy levels. We make only general assumptions about system’s properties and the entropy. System’s constraints other than fixed number of particles can be included by appropriate reduction of system’s state space. For the entropy we consider three generic cases. It can have a maximum in the interior

We introduce the notion of Reeb parallel structure Jacobi operator for real hypersurfaces in the complex hyperbolic quadric \(Q^{*m}=SO^{0}_{2,m}/SO_{2} SO_{m}\), \(m \geqslant 3\), and give a classification theorem for real hypersurfaces in Q∗m, \(m \geqslant 3\), with Reeb parallel structure Jacobi operator.

We describe the main classes of non-signalling bipartite correlations in terms of states on operator system tensor products. This leads to the introduction of another new class of games, called reflexive games, which are characterised as the hardest non-local games that can be won using a given set of strategies. We provide a characterisation of their perfect strategies in terms of operator system

Cecotti and Vafa proposed in 1993 a beautiful idea how to associate spectral numbers\(\alpha _{1},...,\alpha _{n}\in \mathbb {R}\) to real upper triangular n × n matrices S with 1’s on the diagonal and eigenvalues of S− 1St in the unit sphere. Especially, \(\exp (-2\pi i\alpha _{j})\) shall be the eigenvalues of S− 1St. We tried to make their idea rigorous, but we succeeded only partially. This paper

This paper deals with the Cauchy problem of compressible magnetohydrodynamic equations in the whole space ℝ3. We show that if, in addition, the conservation law of the total mass is satisfied (i.e., ρ0 ∈ L1), then the global existence theorem with small density and L3-norm of H0 holds for any γ > 1. It is worth mentioning that the initial velocity can be arbitrarily large and the initial vacuum is

The purpose of the present paper is to analyze correlation structures of the ground states of the Schrödinger operator. We construct Griffiths inequalities for the ground state expectations by applying operator-theoretic correlation inequalities. As an example of such an application, we study the ground state properties of Schrödinger operators.

Spectral properties of random Schrödinger operators are encoded in the average of products of Greens functions. For probability distributions with enough finite moments, the supersymmetric approach offers a useful dual representation. Here we use supersymmetric polar coordinates to derive a dual representation that holds for general distributions. We apply this result to study the density of states

We consider the stochastic higher spin six vertex (SHS6V) model introduced by Corwin and Petrov (Commun. Math. Phys., 343(2), 651–700 2016) with general integer spin parameters I, J. Starting from near stationary initial condition, we prove that the SHS6V model converges to the Kardar-Parisi-Zhang (KPZ) equation under weakly asymmetric scaling. This generalizes the result in Corwin et al. (2018, Theorem

In this paper we consider fourth order differential operators on semi-axis with Robin type boundary condition at zero. Using the commutation method we obtain sharp Lieb-Thirring inequalities for the negative eigenvalues of double multiplicity.

In this article we derive the reflectionless solutions of the 2 + 2 matrix NLS equation with vanishing boundary conditions and four different symmetries by using the matrix triplet method of representing the Marchenko integral kernel in separated form. Apart from using the Marchenko method, these solutions are also verified by direct substitution in the 2 + 2 NLS equation.

It is well-known that a spacetime with its causal relation is a partially ordered set (poset for short). If it is globally hyperbolic, then it is a bicontinuous poset whose the interval topology is the manifold topology. In this work, we will state a new condition on a poset, which is called DS-FI cluster point condition and we show that when a causally simple spacetime \({\mathscr{M}}\) as a poset

In this paper we focus on the large time behaviour of momentum support for a Novikov type equation. It is shown that the momentum support can be large enough as time evolves if the initial data which is compactly supported keeps its sign.

We describe a construction of generalized Maxwell theories – higher analogues of abelian gauge theories – in the factorization algebra formalism of Costello and Gwilliam, allowing for analysis of the structure of local observables. We describe the phenomenon of abelian duality for local observables in these theories as a form of Fourier duality, relating observables in theories with dual abelian gauge

We study a general class of systems of interacting particles that randomly interact to form new or different particles. In addition to the distribution of particles we consider the fluxes, defined as the rescaled number of jumps of each type that take place in a time interval. We prove a dynamic large deviations principle for the fluxes under general assumptions that include mass-action chemical kinetics

Systems of Dyson–Schwinger equation represent the equations of motion in quantum field theory. In this paper, we follow the combinatorial approach and consider Dyson–Schwinger equations as fixed point equations that determine the perturbation series by usage of graph insertion operators. We discuss their properties under the renormalization flow, prove that fixed points are scheme independent, and

We consider a symmetric random walk on the ν-dimensional lattice, whose exit probability from the origin is modified by an antisymmetric perturbation and prove the local central limit theorem for this process. A short-range correction to diffusive behaviour appears in any dimension along with a long-range correction in the one-dimensional case.