# mixing solutions for the muskat problem linkspringer

### Mixing solutions for the Muskat problem SpringerLink

May 05, 2021 10% 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 - link.springer

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

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

Dec 12, 2020 10% 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).

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

10% Mar 08, 2019 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

get price### Article Metrics Mixing solutions for the Muskat problem ...

Jun 23, 2021 10% Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention.

get price### [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)

get price### 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

get price### 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.

get price### [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} }

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, Szé12] applied to the ...

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

May 16, 2016 Abstract: 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.

get price### [2005.08814v1] Mixing solutions for the Muskat problem ...

May 18, 2020 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 ...

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, Szé12] applied to the ...

get price### 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.

get price### 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.

get price### [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))

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### Mixing Solutions for the Muskat Problem

Mixing Solutions for the Muskat Problem Daniel Faraco Universidad Aut onoma de Madrid and IC MAT, Spain [email protected] The talk is based on the joint work with Angel Castro y Diego Cordoba The Muskat Problem describes the evolution of the interphase between two uids evolving through a porous media. The theory is very di erent depending

get price### Mixing solutions for the Muskat problem,Inventiones ...

Mixing solutions for the Muskat problem Inventiones mathematicae ( IF 2.986) Pub Date : 2021-05-05, DOI: 10.1007/s00222-021-01045-1 A. Castro, D. Córdoba, D. Faraco 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.

get price### 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

get price### [1805.12050] Degraded mixing solutions for the Muskat problem

Abstract: 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 ...

get price### [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.

get price### 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).

get price### Scilit Article - Mixing solutions for the Muskat problem ...

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).

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

May 16, 2016 Abstract: 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.

get price### [2005.08814v1] Mixing solutions for the Muskat problem ...

May 18, 2020 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 ...

get price### [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))

get price### 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.

get price### [1805.12050] Degraded mixing solutions for the Muskat problem

Abstract: 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 ...

get price### Mixing Solutions for the Muskat Problem

Mixing Solutions for the Muskat Problem Daniel Faraco Universidad Aut onoma de Madrid and IC MAT, Spain [email protected] The talk is based on the joint work with Angel Castro y Diego Cordoba The Muskat Problem describes the evolution of the interphase between two uids evolving through a porous media. The theory is very di erent depending

get price### Mixing solutions for the Muskat problem,Inventiones ...

Mixing solutions for the Muskat problem Inventiones mathematicae ( IF 2.986) Pub Date : 2021-05-05, DOI: 10.1007/s00222-021-01045-1 A. Castro, D. Córdoba, D. Faraco 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.

get price### 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

get price### 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).

get price### [2102.07451] Localized mixing zone for Muskat bubbles and ...

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].

get price### Degraded mixing solutions for the incompressible porous ...

Apr 26, 2018 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### Piecewise Constant Subsolutions for the Muskat Problem

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get price### Solved: Mixing solutions How much water must be added to 5 ...

Answer to Mixing solutions How much water must be added to 5 pints of a 20% alcohol solution to dilute it to a 15% solution?.

get price### [PDF] Weak Solutions to the Muskat Problem with Surface ...

Inspired by recent works on the threshold dynamics scheme for multi-phase mean curvature flow (by Esedoḡlu–Otto and Laux–Otto), we introduce a novel framework to approximate solutions of the Muskat problem with surface tension. Our approach is based on interpreting the Muskat problem as a gradient flow in a product Wasserstein space. This perspective allows us to construct weak solutions ...

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