Year: 2026
Type: preprint
Abstract: In recent work (arXiv:2610.10341), the authors introduced a framework for studying the vanishing viscosity limit for sequences of weak solutions of the multi-dimensional compressible Navier-Stokes equations to planar shocks of the compressible Euler equations. In this paper, we introduce these methods and apply them to the multi-dimensional viscous Burgers' equation. We show that arbitrarily large viscous shocks enjoy $L^2$-stability among perturbations whose gradients in the directions transverse to the shock are controlled in an appropriate manner. As an application, we study the rate of convergence to the inviscid shock in the vanishing viscosity limit.
Source: arXiv (Cornell University)
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: Stability, Uniqueness, and Existence for Solutions of Hyperbolic Conservation Laws and Nonlinear Wave Equations, Stability Theory for Systems of Hyperbolic Conservation Laws, DMS-EPSRC Collaborative Research: Stability Analysis for Nonlinear Partial Differential Equations across Multiscale Applications, G6291648921, G8533620077
OpenAlex ID: W7222257975