The regularity of the solutions to the Muskat equation: the degenerate regularity near the turnover points

Smoothness and regularity of solutions to PDEs (35B65) PDEs in connection with fluid mechanics (35Q35) Flows in porous media; filtration; seepage (76S05) Analyticity in context of PDEs (35A20) Perturbations in context of PDEs (35B20) Other free boundary flows; Hele-Shaw flows (76D27) Picard-type theorems and generalizations for several complex variables (32H25)

Cites Work

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Rayleigh-Taylor breakdown for the Muskat problem with applications to water waves
A note on stability shifting for the Muskat problem. II: From stable to unstable and back to stable
Interface evolution: the Hele-Shaw and Muskat problems
Lack of uniqueness for weak solutions of the incompressible porous media equation
A maximum principle for the Muskat problem for fluids with different densities
Well-posedness of the Muskat problem with \(H^2\) initial data
Global classical solution of Muskat free boundary problem.
Global well-posedness for the two-dimensional Muskat problem with slope less than 1
On the Muskat problem with viscosity jump: global in time results
Degraded mixing solutions for the Muskat problem
Piecewise constant subsolutions for the Muskat problem
On the global existence for the Muskat problem
On the Cauchy problem for the Muskat equation. II: Critical initial data
Mixing solutions for the Muskat problem with variable speed
Global solutions for the Muskat problem in the scaling invariant Besov space \(\dot{B}_{\infty , 1}^1\)
Self-similar solutions for the Muskat equation
Localized mixing zone for Muskat bubbles and turned interfaces
A paradifferential approach for well-posedness of the Muskat problem
Paralinearization of the Muskat equation and application to the Cauchy problem
Mixing solutions for the Muskat problem
Global regularity for 2D Muskat equations with finite slope
Contour dynamics of incompressible 3-D fluids in a porous medium with different densities
Breakdown of smoothness for the Muskat problem
Two fluid systems in porous media. The encroachment of water into an oil sand.
Endpoint Sobolev theory for the Muskat equation
Regularity of solutions to the Muskat equation
A note on stability shifting for the Muskat problem
On the Muskat problem: Global in time results in 2D and 3D
Global existence, singular solutions, and ill-posedness for the Muskat problem
Relaxation of the incompressible porous media equation
Well-posedness of two-phase Hele–Shaw flow without surface tension
Semiclassical estimates for pseudodifferential operators and the Muskat problem in the unstable regime
On the Cauchy problem for the Muskat equation with non-Lipschitz initial data
Well-posedness of the Muskat problem in subcritical L_p-Sobolev spaces
The Muskat problem with 𝐶¹ data
On the Two‐Dimensional Muskat Problem with Monotone Large Initial Data

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