Analysis of PDEs

Paralinearization of the Muskat Equation and Application to the Cauchy Problem

Publié le - Archive for Rational Mechanics and Analysis

Auteurs : Thomas Alazard, Omar Lazar

We paralinearize the Muskat equation to extract an explicit parabolic evolution equation having a compact form. This result is applied to give a simple proof of the local well-posedness of the Cauchy problem for rough initial data, in homogeneous Sobolev spacesḢ 1 (R) ∩Ḣ s (R) with s > 3/2. This paper is essentially self-contained and does not rely on general results from paradifferential calculus.