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We show strong convergence of the vorticities in the vanishing viscosity limit for the incompressible Navier-Stokes equations on the two-dimensional torus, assuming only that the initial vorticity of the limiting Euler equations is in $L^p$ for some $p>1$. This substantially extends a recent result of Constantin, Drivas and Elgindi, who proved strong convergence in the case $p=infty$. Our proof, which relies on the classical renormalization theory of DiPerna-Lions, is surprisingly simple.
In this article we consider viscous flow in the exterior of an obstacle satisfying the standard no-slip boundary condition at the surface of the obstacle. We seek conditions under which solutions of the Navier-Stokes system in the exterior domain con
We continue the work of Lopes Filho, Mazzucato and Nussenzveig Lopes [LMN], on the vanishing viscosity limit of circularly symmetric viscous flow in a disk with rotating boundary, shown there to converge to the inviscid limit in $L^2$-norm as long as
We study the limiting behavior of viscous incompressible flows when the fluid domain is allowed to expand as the viscosity vanishes. We describe precise conditions under which the limiting flow satisfies the full space Euler equations. The argument i
We consider the damped and driven Navier--Stokes system with stress free boundary conditions and the damped Euler system in a bounded domain $Omegasubsetmathbf{R}^2$. We show that the damped Euler system has a (strong) global attractor in~$H^1(Omega)
Given a strictly hyperbolic, genuinely nonlinear system of conservation laws, we prove the a priori bound $big|u(t,cdot)-u^ve(t,cdot)big|_{L^1}= O(1)(1+t)cdot sqrtve|lnve|$ on the distance between an exact BV solution $u$ and a viscous approximation