Semiclassical estimates for pseudodifferential operators and the Muskat problem in the unstable regime
Víctor Arnaiz, Ángel Castro, Daniel Faraco · Communications in Partial Differential Equations · 2020
We obtain new semiclassical estimates for pseudodifferential operators with low regular symbols. Such symbols appear naturally in a Cauchy Problem related to recent weak solutions to the unstable Muskat problem constructed via convex integration. In particular, our new estimates reveal the tight relation between the speed of opening of the mixing zone and the regularity of the interphase.