The Muskat problem with $C^1$ data

Abstract

In this paper we prove that the Cauchy problem of the Muskat equation is wellposed locally in time for any initial data in ${\dot{C}}^1({\mathbb{R}}^d)\cap L^2({\mathbb{R}}^d)$.

arXiv commentto appear in Transactions of the AMS

References in corpus (5)

• On the global existence for the Muskat problem
• Breakdown of smoothness for the Muskat problem
• On The Muskat Problem With Viscosity Jump: Global In Time Results
• Global wellposedness for the 3D Muskat problem with medium size slope
• Global well-posedness for the three dimensional Muskat problem in the critical Sobolev space

Cited by in corpus (1)

• Global existence and decay of the inhomogeneous Muskat problem with Lipschitz initial data