相关论文: Some properties of a non-hydrostatic stochastic oc…
Stability of travelling waves for the Nagumo equation on the whole line is proven using a new approach via functional inequalities and an implicitely defined phase adaption. The approach can be carried over to obtain pathwise stability of…
The discrete complex Ginzburg-Landau equation is a fundamental model for the dynamics of nonlinear lattices incorporating competitive dissipation and energy gain effects. Such mechanisms are of particular importance for the study of…
In this dissertation, we study the well-posedness of the three-dimensional Lagrangian averaged Navier-Stokes (LANS-$\alpha$) equations. There are two types of LANS-$\alpha$ equations: the anisotropic version in which the fluctuation tensor…
We are concerned with a nonlinear nonautonomous model represented by an equation describing the dynamics of an age-structured population diffusing in a space habitat $O,$ governed by local Lipschitz vital factors and by a stochastic…
This short survey article stems from recent progress on critical cases of stochastic evolution equations in variational formulation with additive, multiplicative or gradient noises. Typical examples appear as the limit cases of the…
We study nonlinear wave equations perturbed by transport noise acting either on the displacement or on the velocity. Such noise models random advection and, under suitable scaling of space covariance, may generate an effective dissipative…
We consider the out-of-equilibrium dynamics of an interacting integrable system in the presence of an external dephasing noise. In the limit of large spatial correlation of the noise, we develop an exact description of the dynamics of the…
When a thermodynamic system is released from any constraint, after some time its evolution will render it into an equilibrium state. Although the description of this relaxation to thermodynamic equilibrium has been attempted through both…
We are concerned with the long-time behavior of classical solutions to the isentropic compressible Navier-Stokes equations in $\mathbb R^3$. Our main results and innovations can be stated as follows: Under the assumption that the density…
We show that, under reasonably mild hypotheses, the solution of the forced--dissipative rotating primitive equations of the ocean loses most of its fast, inertia--gravity, component in the small Rossby number limit as $t\to\infty$. At…
In this article, we study the persistence of properties of a given classical deter-ministic dierential equation under a stochastic perturbation of two distinct forms: external and internal. The rst case corresponds to add a noise term to a…
In this paper, the convergence of the solutions for a discretized linear state-based static peridynamic system to the corresponding continuous solution is analytically proven. To obtain an implementable model, we further apply…
The 2D Euler equations are a simple but rich set of non-linear PDEs that describe the evolution of an ideal inviscid fluid, for which one dimension is negligible. Solving numerically these equations can be extremely demanding. Several…
We consider the two-phase flow model with slip boundary condition in a 3D exterior domains whose boundary is smooth. We establish the global existence of classical solutions of this system provided that the initial energy is suitably small.…
In this paper we are concerned with the initial boundary value problem of the 2, 3-D Navier-Stokes equations with mixed boundary conditions including conditions for velocity, static pressure, stress, rotation and Navier slip condition…
This article establishes local strong well-posedness and global strong well-posedness close to constant equilibria of a model coupling the primitive equations of ocean and atmospheric dynamics with Hibler's viscous-plastic sea ice model. In…
The Navier-Stokes equations in the primitive formulation for incompressible flow describe the evolution of velocity and pressure, without recourse to vorticity. We show that, beyond the finite Leray-Hopf regularity interval, every…
The primitive equations (PEs) model large scale dynamics of the oceans and the atmosphere. While it is by now well-known that the three-dimensional viscous PEs is globally well-posed in Sobolev spaces, and that there are solutions to the…
We consider the isentropic compressible Navier-Stokes-Poisson equations with degenerate viscousities and vacuum in a three-dimensional torus. The local well-posedness of classical solution is established by introducing a "quasi-symmetric…
The goal of this paper is to construct non-trivial steady-state weak solutions of the three dimensional Electron Magnetohydrodynamics equations in the class of $H^s(\mathbb T^3)$ for some small $s > 0$. By exploiting the formulation of the…