Regularity of solutions to the Muskat equation

Abstract

In this paper, we show that if a solution to the Muskat problem in the case of different densities and the same viscosity is sufficiently smooth, then it must be analytic except at the points where a turnover of the fluids happens.

References in corpus (2)

• On the Cauchy problem for the Muskat equation with non-Lipschitz initial data
• Regularity of solutions to the Muskat equation

Cited by in corpus (2)

• Regularity of solutions to the Muskat equation
• Entropy solutions to macroscopic IPM