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 ${\dot{C}}^1({\mathbb{R}}^d)\cap L^2({\mathbb{R}}^d)$.

to appear in Transactions of the AMS

References in corpus (1)

• Global wellposedness for the 3D Muskat problem with medium size slope

Cited by in corpus (1)

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