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

Author
Arnaiz, Víctor; Castro, Ángel; Faraco Hurtado, Danieluntranslated
Entity
UAM. Departamento de Matemáticas
Publisher
Taylor and Francis
Date
2020-10-14
Citation
Communications in Partial Differential Equations 46.1 (2021): 135-164
ISSN
0360-5302 (print); 1532-4133 (online)
DOI
10.1080/03605302.2020.1831019
Funded by
VA, AC and DF have been supported by the Spanish Ministry of Economy under the ICMAT Severo Ochoa grant SEV2015-0554 and VA and AC also by the Europa Excelencia program 28 V. ARNAIZ ET AL. ERC2018-092824. AC is partially supported by the MTM2017-89976-P and the ERC Advanced (Grant no. 788250). D.F is supported by the ERC Advanced (Grant 834728) and by the MTM2017-85934-C3-2-P
Project
info:eu-repo/grantAgreement/EC/H2020/788250/EU//NONFLU; info:eu-repo/grantAgreement/EC/H2020/834728/EU//QUAMAP; Gobierno de España. MTM2017-89976-P
Editor's Version
https://doi.org/10.1080/03605302.2020.1831019
Subjects
Muskat problem; Pseudodifferential operators; Semiclassical analysis; Matemáticas
URI
http://hdl.handle.net/10486/700684
Rights
© 2020 Taylor & Francis Group, LLC.

Licencia de Creative Commons
Esta obra está bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.

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 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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Google™ Scholar:Arnaiz, Víctor - Castro, Ángel - Faraco Hurtado, Daniel

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