Transport equations in Hölder space by vanishing viscosity and applications

2022/09/20 by Honoré, Igor
#35J75 #46E35 #Analysis of PDEs (math.AP) #FOS: Mathematics #Primary: 35K40 #Secondary: 35A02

paper · doi:10.48550/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.

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