Semiclassical estimates for pseudodifferential operators and the Muskat problem in the unstable regime
Analysis of PDEs
2021-04-09 v4
Abstract
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 [CCF16]. In particular, our new estimates reveal the tight relation between the speed of opening of the mixing zone and the regularity of the interphase.
Keywords
Cite
@article{arxiv.2001.06361,
title = {Semiclassical estimates for pseudodifferential operators and the Muskat problem in the unstable regime},
author = {Víctor Arnaiz and Ángel Castro and Daniel Faraco},
journal= {arXiv preprint arXiv:2001.06361},
year = {2021}
}
Comments
24 pages