The Second Iterate of the Muskat Equation in Supercritical Spaces

Abstract

The ill-posedness for the Muskat problem in spaces that are supercritical with respect to the scaling is studied. The main result of the paper establishes that for a sequence of approximations of the Muskat equation obtained via Taylor expansion, their corresponding second Picard's iterate is discontinuous around the origin in a certain family of supercritical spaces approaching a critical space.

29 pages

References in corpus (4)

• On the Cauchy problem for the Muskat equation with non-Lipschitz initial data
• Global wellposedness for the 3D Muskat problem with medium size slope
• Ill-posedness for subcritical hyperdissipative Navier-Stokes equations in the largest critical spaces
• Global existence and decay of the inhomogeneous Muskat problem with Lipschitz initial data