Two-Dimensional Vortex Sheets for the Nonisentropic Euler Equations: Nonlinear Stability
Analysis of PDEs
2020-09-24 v2
Abstract
We show the short-time existence and nonlinear stability of vortex sheets for the nonisentropic compressible Euler equations in two spatial dimensions, based on the weakly linear stability result of Morando--Trebeschi (2008) [20]. The missing normal derivatives are compensated through the equations of the linearized vorticity and entropy when deriving higher-order energy estimates. The proof of the resolution for this nonlinear problem follows from certain \emph{a priori} tame estimates on the effective linear problem {in the usual Sobolev spaces} and a suitable Nash--Moser iteration scheme.
Cite
@article{arxiv.1808.09290,
title = {Two-Dimensional Vortex Sheets for the Nonisentropic Euler Equations: Nonlinear Stability},
author = {Alessandro Morando and Paola Trebeschi and Tao Wang},
journal= {arXiv preprint arXiv:1808.09290},
year = {2020}
}
Comments
to appear in: J. Differential Equations 2018. arXiv admin note: substantial text overlap with arXiv:1707.02672