Nonuniform dependence on initial data for compressible gas dynamics: The Cauchy problem on $\mathbb{R}^2$
Analysis of PDEs
2016-11-21 v1
Abstract
The Cauchy problem for the two dimensional compressible Euler equations with data in the Sobolev space is known to have a unique solution of the same Sobolev class for a short time, and the data-to-solution map is continuous. We prove that the data-to-solution map on the plane is not uniformly continuous on any bounded subset of Sobolev class functions.
Cite
@article{arxiv.1611.05894,
title = {Nonuniform dependence on initial data for compressible gas dynamics: The Cauchy problem on $\mathbb{R}^2$},
author = {John Holmes and Barbara Lee Keyfitz and Feride Tiglay},
journal= {arXiv preprint arXiv:1611.05894},
year = {2016}
}