Mixing solutions for the Muskat problem

• 成果类型: Article
• 署名作者: Castro, A.; Cordoba, D.; Faraco, D.
• 署名单位: Autonomous University of Madrid; Consejo Superior de Investigaciones Cientificas (CSIC); CSIC - Instituto de Ciencias Matematicas (ICMAT); Universidad Carlos III de Madrid; CSIC - Instituto de Ciencia de Materiales de Madrid (ICMM); Complutense University of Madrid; Autonomous University of Madrid
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-021-01045-1
• 发表日期: 2021
• 页码: 251-348
• 关键词: weak solutions; convex integration; euler equations; well-posedness; porous-medium; DISSIPATION; fluid; FLOW

摘要

We prove the existence of mixing solutions of the incompressible porous media equation for all Muskat type H-5 initial data in the fully unstable regime. The proof combines convex integration, contour dynamics and a basic calculus for non smooth semiclassical type pseudodifferential operators which is developed.