Local well-posedness of the $1d$ compressible Navier-Stokes system with rough data

Abstract

This paper presents a new approach to the local well-posedness of the $1d$ compressible Navier-Stokes systems with rough initial data. Our approach is based on establishing some smoothing and Lipschitz-type estimates for the $1d$ parabolic equation with piecewise continuous coefficients.

37 pages