Transport equations in Hölder space by vanishing viscosity and applications
arXiv:2209.09530
Abstract
We obtain a sharp limit Hölder continuity of the solution for the transport equations thanks to a vanishing viscosity analysis. We also derive the same control for parabolic equations and for inviscid Burgers' equation. Eventually, under a structural hypothesis on the coefficients, we provide existence and uniqueness of a Hölder continuous solution.