Bernoulli's type Law of Euler Equations on Sobolev Space in $\mathbb{R}^{3}$

Wei Jin; Xixia Ma

Bernoulli's type Law of Euler Equations on Sobolev Space in $\mathbb{R}^{3}$

Analysis of PDEs 2017-01-26 v4

Authors: Wei Jin , Xixia Ma

Abstract

In this paper, we discuss Bernoulli's principle to the 3-dimensional incompressible Euler equation in a bounded local Lipschitz domain $\Omega\subset\mathbb{R}^{3}$ with a Lipschitz boundary. Using topological properties of the level set and Morse-Sard theorem, we will prove Bernoulli's principle on Sobolev space.

Keywords

Euler equations Bernoulli's principle Sobolev space Lipschitz domain Morse-Sard theorem level set topology

Cite

@article{arxiv.1608.07464,
  title  = {Bernoulli's type Law of Euler Equations on Sobolev Space in $\mathbb{R}^{3}$},
  author = {Wei Jin and Xixia Ma},
  journal= {arXiv preprint arXiv:1608.07464},
  year   = {2017}
}

Comments

the proof has some error

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