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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 $u^ve$, letting the viscosity coefficient $veto 0$. In the proof, starting from $u$ we construct an approximation of the viscous solution $u^ve$ by taking a mollification $u*phi_{strut sqrtve}$ and inserting viscous shock profiles at the locations of finitely many large shocks, for each fixed $ve$. Error estimates are then obtained by introducing new Lyapunov functionals which control shock interactions, interactions between waves of different families and by using sharp decay estimates for positive nonlinear waves.
We investigate the convergence rate in the vanishing viscosity process of the solutions to the subquadratic state-constraint Hamilton-Jacobi equations. We give two different proofs of the fact that, for nonnegative Lipschitz data that vanish on the b
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
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
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