Local well posedness of the Euler-Korteweg equations on $ \mathbb T^d $

Massimiliano Berti; Alberto Maspero; Federico Murgante

Local well posedness of the Euler-Korteweg equations on $ \mathbb T^d $

Analysis of PDEs 2020-07-23 v1

Authors: Massimiliano Berti , Alberto Maspero , Federico Murgante

Abstract

We consider the Euler-Korteweg system with space periodic boundary conditions $x \in \mathbb T^d$ . We prove a local in time existence result of classical solutions for irrotational velocity fields requiring natural minimal regularity assumptions on the initial data.

Keywords

euler-korteweg system periodic boundary local well posedness classical solutions irrotational velocity initial data regularity

Cite

@article{arxiv.2007.11275,
  title  = {Local well posedness of the Euler-Korteweg equations on $ \mathbb T^d $},
  author = {Massimiliano Berti and Alberto Maspero and Federico Murgante},
  journal= {arXiv preprint arXiv:2007.11275},
  year   = {2020}
}

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