On the time of existence of solutions of the Euler-Korteweg system
Analysis of PDEs
2019-06-05 v1
Abstract
Under a natural stability condition on the pressure, it is known that for small irrotational initial data, the solutions of the Euler-Korteweg system are global in time. When the initial velocity has a small rotational part, we obtain a lower bound on the time of existence that depends only on the rotational part. In the zero vorticity limit we recover the previous global well-posedness result. Independently of this analysis, we also provide (in a special case) a simple example of solution that blows up in finite time.
Keywords
Cite
@article{arxiv.1906.01385,
title = {On the time of existence of solutions of the Euler-Korteweg system},
author = {Corentin Audiard},
journal= {arXiv preprint arXiv:1906.01385},
year = {2019}
}