English

Transport equations in H\"older space by vanishing viscosity and applications

Analysis of PDEs 2024-11-20 v3

Abstract

We obtain a sharp limit H\"older 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 H\"older continuous solution.

Keywords

Cite

@article{arxiv.2209.09530,
  title  = {Transport equations in H\"older space by vanishing viscosity and applications},
  author = {Igor Honoré},
  journal= {arXiv preprint arXiv:2209.09530},
  year   = {2024}
}