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# mixing solutions for the muskat problem linkspringer

### Mixing solutions for the Muskat problem SpringerLink

10%  May 05, 2021  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 ...

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

10%  Dec 12, 2020  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, 2016, arXiv:1605.04822 ) and Förster and Székelyhidi (Comm Math Phys 363(3):1051–1080, 2018).

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### Mixing solutions for the Muskat problem - link.springer

10%  Inventiones mathematicae - We prove the existence of mixing solutions of the incompressible porous media equation for all Muskat type...

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### Mixing solutions for the Muskat problem - link.springer

10%  We prove the existence of mixing solutions of the incompressible porous media equation for all Muskat type $$H^5$$ ...

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### Degraded mixing solutions for the Muskat problem

10%  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 submitted in De Lellis and Székelyhidi Jr ...

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### (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 ...

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

May 01, 2016  adshelp[at]cfa.harvard The ADS is operated by the Smithsonian Astrophysical Observatory under NASA Cooperative Agreement NNX16AC86A

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

May 16, 2016  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)

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### Degraded mixing solutions for the Muskat problem Request PDF

Publisher preview available. Degraded mixing solutions for the Muskat problem. March 2019; Calculus of Variations and Partial Differential Equations 58(2)

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### Mixing solutions for the Muskat problem with variable speed

(Mixing solutions for the Muskat problem, 2016, arXiv:1605.04822 ) and Förster and Székelyhidi (Comm Math Phys 363(3):1051–1080, 2018). 1. Introduction

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### [1605.04822v1] Mixing solutions for the Muskat problem

Title: Mixing solutions for the Muskat problem Authors: A. Castro , D. Córdoba , D. Faraco (Submitted on 16 May 2016 (this version), latest version 12 Mar 2021 ( v2 ))

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

Title: Mixing solutions for the Muskat problem Authors: Ángel Castro , Diego Córdoba , Daniel Faraco (Submitted on 16 May 2016 ( v1 ), last revised 12 Mar 2021 (this version, v2))

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### Mixing solutions for the Muskat problem - arxiv-vanity

We prove the existence of mixing solutions of the incompressible porous media equation for all Muskat type H5 initial data in the fully unstable regime.

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### 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, Szé12] applied to the ...

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### Mixing solutions for the Muskat problem : A. Castro : Free ...

We prove the existence of mixing solutions of the incompressible porous media equation for all Muskat type $H^5$ initial data in the fully unstable regime.

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### Mixing solutions for the Muskat problem.

This problem is ill-posed in Sobolev's spaces for an unstable situation in which the part of the fluid with larger density is above. In this course we will present a construction of weak solution of the IPM equation which cosist of the mixing of the two densities for the Muskat problem.

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### [PDF] Mixing solutions for IPM Semantic Scholar

We explain the main steps in the proof of the existence of mixing solutions of the incompressible porous media equation for all Muskat type H5 initial data in the fully unstable regime which appears in [4]. Also we present some numerical simulations about these solutions.

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

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 ...

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### Mixing solutions for the Muskat problem with variable speed

(Mixing solutions for the Muskat problem, 2016, arXiv:1605.04822 ) and Förster and Székelyhidi (Comm Math Phys 363(3):1051–1080, 2018). 1. Introduction

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

Request PDF Mixing solutions for the Muskat problem with variable speed We provide a quick proof of the existence of mixing weak solutions for the Muskat problem with variable mixing speed.

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### [PDF] 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 submitted in De Lellis and Székelyhidi Jr ...

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### export.arxiv

Mixing solutions for the Muskat problem A. Castro, D. C ordoba D. Faraco January 20, 2021 Abstract We prove the existence of mixing solutions of the incompressible porous media

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### Piecewise Constant Subsolutions for the Muskat Problem ...

We show the existence of infinitely many admissible weak solutions for the incompressible porous media equations for all Muskat-type initial data with $${C^{3,\alpha}}$$-regularity of the interface in the unstable regime and for all non-horizontal data with $${C^{3,\alpha}}$$-regularity in the stable regime.

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### Mixing solutions for the Muskat problem - arxiv-vanity

We prove the existence of mixing solutions of the incompressible porous media equation for all Muskat type H5 initial data in the fully unstable regime.

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### [PDF] Mixing solutions for the Muskat problem with ...

Mixing solutions for the Muskat problem with variable speed @article{Noisette2020MixingSF, title={Mixing solutions for the Muskat problem with variable speed}, author={Florent Noisette and L. Sz{\'e}kelyhidi}, journal={arXiv: Analysis of PDEs}, year={2020} }

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

Title: Mixing solutions for the Muskat problem with variable speed. Authors: Florent Noisette, László Székelyhidi Jr (Submitted on 18 May 2020) Abstract: 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 ...

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### 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, Szé12] applied to the ...

get price

### [PDF] 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 submitted in De Lellis and Székelyhidi Jr ...

get price

### Mixing solutions for the Muskat problem.

This problem is ill-posed in Sobolev's spaces for an unstable situation in which the part of the fluid with larger density is above. In this course we will present a construction of weak solution of the IPM equation which cosist of the mixing of the two densities for the Muskat problem.

get price

### Degraded mixing solutions for the Muskat problem Papers ...

Degraded mixing solutions for the Muskat problem 30 May 2018 Castro Ángel, Faraco Daniel , Mengual Francisco Edit social preview. 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. ...

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### a2c [1605.04822] Mixing solutions for the Muskat problem

[1605.04822] Mixing solutions for the Muskat problem Abstract We prove the existence of mixing solutions of the incompressible porous media equation for all Muskat type H5 initial data in the fully unstable regime. Related: TFIDF [1603.03325] ...

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

Abstract. 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}.Comment: 20 page

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### 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.

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

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

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

Acknowledgements AC and DF were partially supported by ICMAT Severo Ochoa Projects SEV-2011-0087 and SEV-2015-556, and by the ERC Grant 307179-GFTIPFD. DF and FM were partially supported by the Grant MTM2017-85934-C3-2-P (Spain). AC were partially supported by the Grant MTM2014-59488-P (Spain) and DF by the Grants MTM2014-57769-P-1 and MTM2014-57769-P-3 (Spain).

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### arXiv

Mixing solutions for the Muskat problem A. Castro, D. C ordoba D. Faraco August 15, 2018 Abstract We prove the existence of mixing solutions of the incompressible porous media e

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### [2102.07451v1] Localized mixing zone for Muskat bubbles ...

Abstract: We construct mixing solutions to the incompressible porous media equation starting from Muskat type data in the partially unstable regime. In particular, we consider bubble and turned type interfaces with Sobolev regularity. As a by-product, we prove the continuation of the evolution of IPM after the Rayleigh-Taylor and smoothness breakdown exhibited in [18,17].

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