相关论文: On The Muskat Problem With Viscosity Jump: Global …
The inhomogeneous Muskat problem models the dynamics of an interface between two fluids of differing characteristics inside a non-uniform porous medium. We consider the case of a porous media with a permeability jump across a horizontal…
In this paper we consider the Muskat problem describing the motion of two unbounded immiscible fluid layers with equal viscosities in vertical or horizontal two-dimensional geometries. We first prove that the mathematical model can be…
This paper considers the three dimensional Muskat problem in the stable regime. We obtain a conservation law which provides an $L^2$ maximum principle for the fluid interface. We also show global in time existence for strong and weak…
We study the two-dimensional multiphase Muskat problem describing the motion of three immiscible fluids with equal viscosities in a vertical homogeneous porous medium identified with $\mathbb{R}^2$ under the effect of gravity. We first…
We prove local well-posedness for the Muskat problem on the half-plane, which models motion of an interface between two fluids of distinct densities (e.g., oil and water) in a porous medium (e.g., an aquifer) that sits atop an impermeable…
In this paper, we study the dynamics of a two-dimensional viscous fluid evolving through a porous medium or a Hele-Shaw cell, driven by gravity and surface tension. A key feature of this study is that the fluid is confined within a vessel…
We study the dynamics of the interface between two incompressible fluids in a two-dimensional porous medium whose flow is modeled by the Muskat equations. For the two-phase Muskat problem, we establish global well-posedness and decay to…
We first prove local-in-time well-posedness for the Muskat problem, modeling fluid flow in a two-dimensional inhomogeneous porous media. The permeability of the porous medium is described by a step function, with a jump discontinuity across…
We study the Muskat problem on the half-plane, which models motion of an interface between two fluids of distinct densities (e.g., oil and water) in a porous medium (e.g., an aquifer) that sits atop an impermeable layer (e.g., bedrock).…
In this work we study the inhomogeneous Muskat problem, \emph{i.e.} the evolution of an internal wave between two different fluids in a porous medium with discontinuous permeability. In particular, under precise conditions on the initial…
In this paper, we establish the existence of global self-similar solutions to the 3D Muskat equation when the two fluids have the same viscosity but different densities. These self-similar solutions are globally defined in both space and…
The free boundary problem for a two-dimensional fluid filtered in porous media is studied. This is known as the one-phase Muskat problem and is mathematically equivalent to the vertical Hele-Shaw problem driven by gravity force. We prove…
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 viscosities under the influence of gravity in which one…
We address a generalised three-dimensional $\alpha$-Muskat model that comes from the fluid interface problem given by two incompressible fluids with different densities in the stable regime. We establish local-in-time wellposedness when…
We consider the fluid interface problem given by two incompressible fluids with different densities evolving by Darcy's law. This scenario is known as the Muskat problem for fluids with the same viscosities, being in two dimensions…
We consider the 2D Muskat equation for the interface between two constant density fluids in an incompressible porous medium, with velocity given by Darcy's law. We establish that as long as the slope of the interface between the two fluids…
In this paper we study the two-dimensional multiphase Muskat problem describing the motion of three immiscible fluids with general viscosities in a vertical homogeneous porous medium under the influence of gravity. Employing Rellich type…
The Muskat problem models the dynamics of the interface between two incompressible immiscible fluids with different constant densities. In this work we prove three results. First we prove an $L^2(\R)$ maximum principle, in the form of a new…
We consider the evolution of two incompressible, immiscible fluids with different densities in porous media, known as the Muskat problem [21], which in two dimensions is analogous to the Hele-Shaw cell [26]. We establish, for a class of…
We study the Muskat problem describing the spatially periodic motion of two fluids with equal viscosities under the effect of gravity in a vertical unbounded two-dimensional geometry. We first prove that the classical formulation of the…