Endpoint Sobolev Theory for the Muskat Equation

This paper is devoted to the study of solutions with critical regularity for the two-dimensional Muskat equation. We prove that the Cauchy problem is well-posed on the endpoint Sobolev space of L 2 functions with three-half derivative in L 2 . This result is optimal with respect to the scaling of th...

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Veröffentlicht in:	Communications in mathematical physics 2023-02, Vol.397 (3), p.1043-1102
Hauptverfasser:	Alazard, Thomas, Nguyen, Quoc-Hung
Format:	Artikel
Sprache:	eng
Schlagworte:	Analysis of PDEs Cauchy problems Classical and Quantum Gravitation Complex Systems Flow mapping Mathematical and Computational Physics Mathematical Physics Mathematics Physics Physics and Astronomy Quantum Physics Relativity Theory Sobolev space Theoretical
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