A paradifferential approach for well-posedness of the Muskat problem
We study the Muskat problem for one fluid or two fluids, with or without viscosity jump, with or
without rigid boundaries, and in arbitrary space dimension d of the interface. The Muskat …
without rigid boundaries, and in arbitrary space dimension d of the interface. The Muskat …
[BOOK][B] Global regularity for gravity unstable Muskat bubbles
In this paper, we study the dynamics of fluids in porous media governed by Darcy's law: the
Muskat problem. We consider the setting of two immiscible fluids of different densities and …
Muskat problem. We consider the setting of two immiscible fluids of different densities and …
Global well-posedness for the three dimensional Muskat problem in the critical Sobolev space
We prove that the three dimensional stable Muskat problem is globally well-posed in the
critical Sobolev space H˙ 2∩ W˙ 1,∞ provided that the semi-norm‖ f 0‖ H˙ 2 is small …
critical Sobolev space H˙ 2∩ W˙ 1,∞ provided that the semi-norm‖ f 0‖ H˙ 2 is small …
[HTML][HTML] Surface tension stabilization of the Rayleigh-Taylor instability for a fluid layer in a porous medium
This paper studies the dynamics of an incompressible fluid driven by gravity and capillarity
forces in a porous medium. The main interest is the stabilization of the fluid in Rayleigh …
forces in a porous medium. The main interest is the stabilization of the fluid in Rayleigh …
Global well‐posedness for the one‐phase Muskat problem
The free boundary problem for a two‐dimensional fluid permeating a porous medium is
studied. This is known as the one‐phase Muskat problem and is mathematically equivalent …
studied. This is known as the one‐phase Muskat problem and is mathematically equivalent …
On Nonlinear Stability of Muskat Bubbles
In this paper we consider gravity-capillarity Muskat bubbles in 2D. We obtain a new
approach to improve our result in [1]. Due to a new bubble-adapted formulation, the …
approach to improve our result in [1]. Due to a new bubble-adapted formulation, the …
Motility and morphodynamics of confined cells
We introduce a minimal hydrodynamic model of polarization, migration, and deformation of a
biological cell confined between two parallel surfaces. In our model, the cell is driven out of …
biological cell confined between two parallel surfaces. In our model, the cell is driven out of …
Self-similar solutions for the Muskat equation
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The Hele-Shaw semi-flow
We prove that the Cauchy problem is well-posed in a strong sense and in a general setting.
Our main result is the construction of an abstract semi-flow for the Hele-Shaw problem within …
Our main result is the construction of an abstract semi-flow for the Hele-Shaw problem within …
The vanishing surface tension limit of the Muskat problem
The Muskat problem, in its general setting, concerns the interface evolution between two
incompressible fluids of different densities and viscosities in porous media. The interface …
incompressible fluids of different densities and viscosities in porous media. The interface …