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

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 rel...

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Detalles Bibliográficos
Autor: Arnaiz, Víctor
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2021
País:España
Institución:Consejo Superior de Investigaciones Científicas (CSIC)
Repositorio:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/233053
Acceso en línea:http://hdl.handle.net/10261/233053
Access Level:acceso abierto
Descripción
Sumario: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.