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arXiv · 2001.06361

Semiclassical estimates for pseudodifferential operators and the Muskat problem in the unstable regime

Víctor Arnaiz·Ángel Castro·Daniel Faraco
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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.

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Víctor Arnaiz, Ángel Castro, Daniel Faraco. 2020-01-17. Semiclassical estimates for pseudodifferential operators and the Muskat problem in the unstable regime. https://doi.org/10.1080/03605302.2020.1831019

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