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math.APNov 20, 2022
8
citations (OpenAlex)
authors
  • Jia Shi
institutions
  • Massachusetts Institute of Technology
arXiv abstractPDF
paper

Regularity of solutions to the Muskat equation

arXiv:2211.11006 · doi:10.1007/s00205-023-01862-z

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.

References in corpus (13)

  • On the global existence for the Muskat problem
  • Breakdown of smoothness for the Muskat problem
  • Lack of uniqueness for weak solutions of the incompressible porous media equation
  • The Muskat problem in 2D: equivalence of formulations, well-posedness, and regularity results
  • On The Muskat Problem With Viscosity Jump: Global In Time Results
  • Global well-posedness for the 2D Muskat problem with slope less than 1
  • Paralinearization of the Muskat equation and application to the Cauchy problem
  • A note on stability shifting for the Muskat problem II: Stable to Unstable and back to Stable
  • Piecewise constant subsolutions for the Muskat problem
  • A note on stability shifting for the Muskat problem
  • On the Cauchy problem for the Muskat equation with non-Lipschitz initial data
  • Well-posedness of the Muskat problem in subcritical Lp​-Sobolev spaces
  • Regularity of solutions to the Muskat equation

Cited by in corpus (2)

  • Regularity of solutions to the Muskat equation
  • Entropy solutions to macroscopic IPM
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