Bernoulli's type Law of Euler Equations on Sobolev Space in   $\mathbb{R}^{3}$
  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. 
Wei Jin, Xixia Ma
math.AP