相关论文: On the inviscid limit of the 2D Euler equations wi…
In this paper, we consider the inviscid limit problem to the higher dimensional incompressible Navier-Stokes equations in the whole space. It was proved in \cite[J. Funct. Anal., 276 (2019)]{GZ} that given initial data $u_0\in B^{s}_{p,r}$…
In this paper, we consider the inviscid limit problem to the higher dimensional incompressible Navier--Stokes equations in the whole space. It is shown in [Guo, Li, Yin: J. Funct. Anal., 276 (2019)] that given initial data $u_0\in…
This paper is devoted to the study of the Cauchy problem for the stratified Navier-Stokes system in space dimension three. In the first part of the paper, we prove the existence of a unique global solution $(v_\nu,\rho_\nu)$ for this system…
We prove the inviscid limit of the incompressible Navier-Stokes equations in the same topology of Besov spaces as the initial data. The proof is based on proving the continuous dependence of the Navier-Stokes equations uniformly with…
In this paper we prove the uniform-in-time $L^p$ convergence in the inviscid limit of a family $\omega^\nu$ of solutions of the $2D$ Navier-Stokes equations towards a renormalized/Lagrangian solution $\omega$ of the Euler equations. We also…
Chemin has shown that solutions of the Navier-Stokes equations in the plane for an incompressible fluid whose initial vorticity is bounded and lies in L^2 converge in the zero-viscosity limit in the L^2-norm to a solution of the Euler…
This work is concerned with 2D-Navier Stokes equations in a multiply-connected bounded domain with permeable walls. The permeability is described by a Navier type condition. Our aim is to show that the inviscid limit is a solution of the…
We prove that any weak space-time $L^2$ vanishing viscosity limit of a sequence of strong solutions of Navier-Stokes equations in a bounded domain of ${\mathbb{R}}^2$ satisfies the Euler equation if the solutions' local enstrophies are…
We prove the existence and some moment estimates for an invariant measure $\mu$ for the two-dimensional ($2$D) deterministic Euler equations on the unbounded domain $\mathbb R^2$ and with highly regular initial data. The result is achieved…
We consider the inviscid limit for the two-dimensional Navier--Stokes equations in the class of integrable and bounded vorticity fields. It is expected that the difference between the Navier--Stokes and Euler velocity fields vanishes in…
We study inviscid limits of invariant measures for the 2D Stochastic Navier-Stokes equations. As shown in \cite{Kuksin2004} the noise scaling $\sqrt{{\nu}}$ is the only one which leads to non-trivial limiting measures, which are invariant…
We consider the convergence in the $L^2$ norm, uniformly in time, of the Navier-Stokes equations with Dirichlet boundary conditions to the Euler equations with slip boundary conditions. We prove that if the Oleinik conditions of no…
We consider stochastic Navier-Stokes equations in a 2D-bounded domain with the Navier with friction boundary condition. We establish the existence and the uniqueness of the solutions and study the vanishing viscosity limit. More precisely,…
We study the inviscid limit problem for the incompressible Navier-Stokes equation on a half-plane with a Navier boundary condition depending on the viscosity. On one hand, we prove the $L^2$ convergence of Leray solutions to the solution of…
Consider the steady solution to the incompressible Euler equation $\bar u=Ae_1$ in the periodic tunnel $\Omega=\mathbb T^{d-1}\times(0,1)$ in dimension $d=2,3$. Consider now the family of solutions $u^\nu$ to the associated Navier-Stokes…
We analyze the two-dimensional incompressible Navier-Stokes equations on a smooth, bounded domain with Navier boundary conditions. Starting from an initial vorticity in $L^p$ with $p>2$, we show strong convergence of the vorticity in the…
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., $\rho^\delta$…
We consider in a smooth and bounded two dimensional domain the convergence in the $L^2$ norm, uniformly in time, of the solution of the stochastic Navier-Stokes equations with additive noise and no-slip boundary conditions to the solution…
In [1], T. Clopeau, A. Mikeli\'c, and R. Robert studied the inviscid limit of the 2D incompressible Navier-Stokes equations in a bounded domain subject to Navier friction-type boundary conditions. They proved that the inviscid limit…
In this paper, we consider the inviscid limit of the incompressible Navier-Stokes equations in a smooth, bounded and simply connected domain $\Omega \subset \mathbb{R}^d, d=2,3$. We prove that for a vortex patch initial data the weak Leray…