Desingularization of small moving corners for the Muskat equation

PDEs in connection with fluid mechanics (35Q35) Flows in porous media; filtration; seepage (76S05) Other free boundary flows; Hele-Shaw flows (76D27) Moving boundary problems for PDEs (35R37) Liquid-liquid two component flows (76T06)

Cites Work

Unnamed Item
Splash singularities for the one-phase Muskat problem in stable regimes
Porous media: The Muskat problem in three dimensions
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
Well-posedness of the Muskat problem with $H^2$ initial data
Layer potentials and regularity for the Dirichlet problem for Laplace's equation in Lipschitz domains
Global classical solution of Muskat free boundary problem.
The Muskat problem in two dimensions: equivalence of formulations, well-posedness, and regularity results
Global well-posedness for the two-dimensional Muskat problem with slope less than 1
A survey for the Muskat problem and a new estimate
On the Muskat problem with viscosity jump: global in time results
On the global existence for the Muskat problem
On the Cauchy problem for the Muskat equation. II: Critical initial data
Global solutions for the Muskat problem in the scaling invariant Besov space $\dot{B}_{\infty , 1}^1$
Rigidity of acute angled corners for one phase Muskat interfaces
Quasilinearization of the 3D Muskat equation, and applications to the critical Cauchy problem
Self-similar solutions for the Muskat equation
A paradifferential approach for well-posedness of the Muskat problem
Paralinearization of the Muskat equation and application to the Cauchy 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
The flow of homogeneous fluids through porous media.
Global well-posedness for the three dimensional Muskat problem in the critical Sobolev space
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
Regularity of one-phase Stefan problem near Lipschitz initial data
Viscous displacement in porous media: the Muskat problem in 2D
Well-posedness of two-phase Hele–Shaw flow without surface tension
The Two-Phase Hele-Shaw Problem with a Nonregular Initial Interface and Without Surface Tension
Growth in the Muskat problem
On the Cauchy problem for the Muskat equation with non-Lipschitz initial data
Global well-posedness for the 2D stable Muskat problem in $H^{3/2}$
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
Waiting time phenomena of the Hele-Shaw and the Stefan problem