Higher Regularity Theory for a Mixed-Type Parabolic Equation
Analysis of PDEs
2022-12-20 v1
Abstract
In this paper, we study the higher regularity theory of a mixed-type parabolic problem. We extend the recent work of \cite{DMR} to construct solutions that have an arbitrary number of derivatives in Sobolev spaces. To achieve this, we introduce a counting argument based on a quantity called the "degree". In the second part of this paper, we apply this existence theory to the Prandtl system near the classical Falkner-Skan self-similar profiles in order to supplement the stability analysis of \cite{IM22} with a rigorous construction argument.
Keywords
Cite
@article{arxiv.2212.08735,
title = {Higher Regularity Theory for a Mixed-Type Parabolic Equation},
author = {Sameer Iyer and Nader Masmoudi},
journal= {arXiv preprint arXiv:2212.08735},
year = {2022}
}
Comments
36 pages. Companion paper to arXiv:2203.02845