## Mixing solutions for the Muskat problem linkspringer

# Mixing solutions for the Muskat problem linkspringer

### Mixing solutions for the Muskat problem SpringerLink

2021-5-5 Then there exist infinitely many “mixing solutions” starting with the inital data of Muskat type given by \(\Gamma (0)\) (in the fully unstable regime) for the IPM system. Remark 1.2. The existence of such mixing solutions was predicted by Otto in . In this pioneering paper, Otto discretizes the problem and present a relaxation in the ...

get price### Mixing solutions for the Muskat problem with variable ...

2020-12-12 We provide a quick proof of the existence of mixing weak solutions for the Muskat problem with variable mixing speed. Our proof is considerably shorter and extends previous results in Castro et al. (Mixing solutions for the Muskat problem

get price### (PDF) Mixing solutions for the Muskat problem

a mixing domain Ω mix (t) such that for every space-time ball contained in the mixing area the density will take both values ρ + and ρ − . We will call these solutions mixing solutions (see ...

get price### [1605.04822] Mixing solutions for the Muskat problem

2016-5-16 73 pages, 2 figures. This version includes the case of variable opening of the mixing zone and emphasizes the semiclassical analysis viewpoint: Subjects: Analysis of PDEs (math.AP) Cite as: arXiv:1605.04822 [math.AP] (or arXiv:1605.04822v2 [math.AP] for this version)

get price### [2005.08814] Mixing solutions for the Muskat problem with ...

2020-5-18 We provide a quick proof of the existence of mixing weak solutions for the Muskat problem with variable mixing speed. Our proof is considerably shorter and extends previous results in \\cite{ccf:ipm} and \\cite{fsz:ipm}.

get price### (PDF) Mixing solutions for the Muskat problem with ...

Mixing solutions for the Muskat problem separation in the two dynamics: once a mixing zone appears, the pseudo-interface is a matter of arbitrary choice, the only relevant object for the system ...

get price### Mixing solutions for the Muskat problem - NASA/ADS

adshelp[at]cfa.harvard The ADS is operated by the Smithsonian Astrophysical Observatory under NASA Cooperative Agreement NNX16AC86A

get price### Mixing solutions for the Muskat problem - CORE Reader

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get price### Degraded mixing solutions for the Muskat problem A.

2020-12-12 Degraded mixing solutions for the Muskat problem A. Castro, D. Faraco, F. Mengual November 13, 2019 Abstract We prove the existence of in nitely many mixing solutions for the Muskat problem in the fully unstable regime displaying a linearly degraded macroscopic behaviour inside the mixing zone. In fact, we estimate the volume proportion of each

get price### Degraded mixing solutions for the Muskat problem - CORE

Degraded mixing solutions for the Muskat problem - CORE Reader

get price### Mixing solutions for the Muskat problem - CORE Reader

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get price### Stability shifting and mixing solutions for the Muskat ...

2020-4-24 Stability shifting and mixing solutions for the Muskat problem Cordoba, Diego; ICMat-CSIC The Muskat equation governs the motion of an interface separation of two incompressible fluids in a porous media. In this talk I will present the following recent results:

get price### Degraded mixing solutions for the Muskat problem - CORE

Degraded mixing solutions for the Muskat problem - CORE Reader

get price### Degraded mixing solutions for the Muskat problem

We prove the existence of infinitely many mixing solutions for the Muskat problem in the fully unstable regime displaying a linearly degraded macroscopic behaviour inside the mixing zone. In fact, we estimate the volume proportion of each fluid in every rectangle of the mixing zone. The proof is a refined version of the convex integration scheme presented in [DS10, Sze12] applied to the ...

get price### DIGITAL.CSIC: Degraded mixing solutions for the Muskat problem

2020-3-6 The proof is a refined version of the convex integration scheme submitted in De Lellis and Székelyhidi Jr. (Arch Ration Mech Anal 195:225–260, 2010), Székelyhidi (Ann Sci Éc Norm Supér 45(3):491–509, 2012) applied to the subsolution in Castro et al. (Mixing solutions for the Muskat problem, arXiv:1605.04822, 2016).

get price### Rayleigh-Taylor breakdown for the Muskat problem with ...

The Muskat problem models the evolution of the interface between two different fluids in porous media. The Rayleigh-Taylor condition is natural to reach linear stability of the Muskat problem. We show that the Rayleigh-Taylor condition may hold initially but break down in finite time.

get price### WEAK SOLUTIONS TO THE MUSKAT PROBLEM WITH

2021-1-19 construct global-in-time weak solutions to the Muskat problem (MP 2), which exist past the formation of singularities. To construct global-in-time solutions, we exploit the gradient ow structure of the Muskat problem. As noted by Otto in [28,29], Darcy’s law

get price### WEAK SOLUTIONS TO THE MUSKAT PROBLEM WITH

2020-9-15 WEAK SOLUTIONS TO THE MUSKAT PROBLEM WITH SURFACE TENSION VIA OPTIMAL TRANSPORT 3 Indeed, it is not easy to obtain a complete characterization of the solutions to the minimizing move-ments problem (7). The interaction energy (5) is su ciently non-convex that problem (7) is non-convex for any ˝>0.

get price### Global Existence, Singular Solutions, and Ill-Posedness ...

2004-12-8 Hele-Shaw problem (the one-phase version of the Muskat problem), there are few nontrivial exact solutions or analytic results for the Muskat problem. For the stable, forward Muskat problem, in which the higher-viscosity ﬂuid expands into the lower-viscosity ﬂuid, we

get price### AMS :: Transactions of the American Mathematical Society

Well-posedness and decay to equilibrium for the Muskat problem with discontinuous permeability ... Mixing solutions for the Muskat problem, arXiv:1605.04822, (2016). Ángel Castro, Diego Córdoba, Charles Fefferman, and Francisco Gancedo ... and Steve Shkoller, Global existence and decay for solutions of the Hele-Shaw flow with injection ...

get price### Asymptotics for the Muskat problem, Journal of Engineering ...

2010-4-29 Asymptotics for the Muskat problem Asymptotics for the Muskat problem Booth, R. 2010-04-29 00:00:00 The Muskat problem is a simple model for the displacement of one fluid by another in a porous medium or Hele-Shaw cell. Solutions of the problem are unstable to small-wavelength disturbances, and there is evidence that the problem is ill-posed.

get price### [PDF] The Muskat problem in two dimensions: equivalence of ...

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 formulated as an evolution problem for the sharp interface separating the two fluids, which turns out to be, in a suitable functional analytic setting ...

get price### Local and global dynamics of concentrated vortices ...

Stability shifting and mixing solutions for the Muskat problem - Diego Córdoba 10:00 - 11:00: Exploring new solutions to the incompressible Euler equations - Juan Soler 11:00 - 11:30: Pause café 11:30 - 12:30: Reconnection of vortex structures in the 3D Navier-Stokes equations - Alberto Enciso

get price### Regularity theory for elliptic and parabolic systems and ...

2018-6-4 I will present the construction of degraded mixing solutions for the IPM system. This system models the dynamics of an incompressible and viscous fluid in a porous media and under the gravitational force. When the initial density of the fluid just take two values the existence of solutions for IPM is known as the Muskat problem.

get price### Publications László Székelyhidi Jr.

2021-8-13 Noisette, Florent and Székelyhidi, László: Mixing solutions for the Muskat problem with variable speed In: Journal of evolution equations , Vol. not yet known, pp. not yet known

get price### Javier Gómez-Serrano - Papers

2021-7-22 Global smooth solutions for the inviscid SQG equation, with A. Castro and D. Córdoba. Memoirs of the AMS, 266, 1292, 89 pp (2020). A note on stability shifting for the Muskat problem II: Stable to Unstable and back to Stable, with D. Córdoba and A. Zlatoš. Analysis

get price### Semianalytical solutions for cocurrent and countercurrent ...

section 4, we compare the obtained solutions against the nu-merical reference solution for the cases of cocurrent and countercurrent imbibition and for the capillary-free limit, the Buckley-Leverett problem [Buckley and Leverett, 1942], and then ﬁnish with some conclusions. 2. Preliminaries 2.1. Problem Formulation and Assumptions

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