Regularity of solutions to the Muskat equation

DOI10.1007/S00205-023-01862-ZarXiv2211.11006MaRDI QIDQ6417860

Publication date: 20 November 2022

Abstract: In this paper, we show that if a solution to the Muskat problem in the case of different densities and the same viscosity is sufficiently smooth, then it must be analytic except at the points where a turnover of the fluids happens.

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) PDEs in connection with fluid mechanics (35Q35) Flows in porous media; filtration; seepage (76S05) Other free boundary flows; Hele-Shaw flows (76D27)

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