منابع مشابه
On the global existence for the Muskat problem
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(R) maximum principle, in the form of a new “log” conservation law (3) which is satisfied by the equation (1) for the interface. Our second result is a proof of global existence of Lipschitz continuous sol...
متن کاملPorous media: the Muskat problem in 3D
The Muskat problem involves filtration of two incompressible fluids throughout a porous medium. In this paper we shall discuss in 3-D the relevance of the RayleighTaylor condition, and the topology of the initial interface, in order to prove its local existence in Sobolev spaces.
متن کاملA note on stability shifting for the Muskat problem.
In this note, we show that there exist solutions of the Muskat problem that shift stability regimes: they start unstable, then become stable and finally return to the unstable regime. We also exhibit numerical evidence of solutions with medium-sized L(∞) norm of the derivative of the initial condition that develop a turning singularity.
متن کاملThe Domain of Parabolicity for the Muskat Problem
Abstra t. We address the well-posedness of the Muskat problem in a periodi geometry and in a setting whi h allows us to onsider general initial and boundary data, gravity e e ts, as well as surfa e tension e e ts. In the absen e of surfa e tension we prove that the Rayleigh-Taylor ondition identi es a domain of paraboli ity for the Muskat problem. This property is used to establish the well-pos...
متن کاملWell-posedness of the Muskat problem with H2 initial data
Article history: Received 30 December 2014 Accepted 13 August 2015 Available online xxxx Communicated by Charles Fefferman MSC: 35R35 35Q35 35S10 76B03
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ژورنال
عنوان ژورنال: Evolution Equations and Control Theory
سال: 2016
ISSN: 2163-2480
DOI: 10.3934/eect.2016022