Mixing solutions for the Muskat problem. ... A. Castro, D. C´ ordoba D. F ... The method of the proof seems robust to prove existence of weak solutions in a num ber of free.

Get PriceDOI: 10.1007/S00222-021-01045-1 Corpus ID: 119303915. Mixing solutions for the Muskat problem @article{Castro2016MixingSF, title={Mixing solutions for the Muskat problem}, author={{\'A}ngel Castro and Diego C'ordoba and Daniel Faraco}, journal={arXiv: Analysis of PDEs}, year={2016} }

Get Price2021-5-5 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 Price2020-12-12 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 PriceWe 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 Price2016-5-16 Please join the Simons Foundation and our generous member organizations in supporting arXiv during our giving campaign September 23-27. 100% of your contribution will fund improvements and new initiatives to benefit arXiv's global scientific community.

Get Price2020-12-12 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, 2016, arXiv:1605.04822 ) and Förster and Székelyhidi (Comm Math Phys 363(3):1051–1080, 2018).

Get PricePDF We provide a quick proof of the existence of mixing weak solutions for the Muskat problem with variable mixing speed. Our proof is considerably... Find, read and cite all the research you ...

Get Price2016-5-1 adshelp[at]cfa.harvard The ADS is operated by the Smithsonian Astrophysical Observatory under NASA Cooperative Agreement NNX16AC86A

Get Price2018-5-31 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 Price2021-10-7 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 Price2018-5-31 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 Price2020-4-24 On the global existence for the Muskat problem On the Muskat problem: global in time results in 2D and 3D Part III: Large time Decay for the Muskat problem Large time Decay Estimates for the Muskat equation Part IV: Absence of singularity formation for the Muskat problem Absence of splash singularities for SQG sharp fronts and the Muskat problem

Get PriceThe 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 Price2019-3-17 The Muskat problem then became the first incompressible model where blow-up for solutions with initial data in well-posed scenarios had been proven rigorously. Specifically, in the 2D density jump case, solutions starting in stable situation (denser fluid below a graph) become instantly analytic and move to unstable regimes in finite time [10] .

Get PriceThe 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. As a consequence of the method used, we prove the existence of water waves turning. Pages 909-948 by Ángel Castro, Diego Córdoba, Charles Fefferman, Francisco ...

Get Price2020-11-16 Semiclassical estimates for pseudodifferential operators and the Muskat problem in the unstable regime Víctor Arnaiz , Ángel Castro Daniel Faraco Pages: 135-164

Get Price2021-10-13 11. Absence of squirt singularities for the multi-phase Muskat problem, con D. C ordo-ba. Comm. Math. Phys., 299, no. 2, 561-575, 2010 12. Lack of uniqueness for weak solutions of the incompressible porous media equation,

Get Price2017-1-17 Incompressible Euler equations Some facts: • To any given suff. smooth initial data there exists, at least for a short time, a unique suff. smooth solution (Lichtenstein 1930s, Kato 1980s). • For any suff. smooth solution, the energy is constant in time (classical). • There exist non-trivial weak solutions with compact support in time (Scheffer 1993).

Get Price2014-9-19 We consider entropy solutions to the Cauchy problem for the isentropic compressible Euler equations in the spatially periodic case. In more than one space dimension, the methods developed by De Lellis–Székelyhidi enable us to show here failure of uniqueness on a finite time-interval for entropy solutions starting from any continuously differentiable initial density and suitably constructed ...

Get Price2021-1-18 Well-posedness of the Muskat problem in subcritical Lp-Sobolev spaces Skip to main content Accessibility help We use cookies to distinguish you from other users and to provide you with a better experience on our websites.

Get Price2019-3-17 The Muskat problem then became the first incompressible model where blow-up for solutions with initial data in well-posed scenarios had been proven rigorously. Specifically, in the 2D density jump case, solutions starting in stable situation (denser fluid below a graph) become instantly analytic and move to unstable regimes in finite time [10] .

Get Price2021-11-11 We review some recent results on the Muskat problem modelling multiphase flow in porous media. Furthermore, we prove a new regularity criteria in terms of some norms of the initial data in critical spaces (˙W1,∞ and ˙H3/2).

Get PriceÁngel Castro, Diego Córdoba, Charles Fefferman, Francisco Gancedo, and María López-Fernández, Rayleigh-Taylor breakdown for the Muskat problem with applications to water waves, Ann. of Math. (2) 175 (2012), no. 2, 909–948. MR 2993754, DOI 10.4007/annals.2012.175.2.9

Get Price2021-5-13 Abstract: The Muskat problem studies the evolution of the interface between two incompressible, immiscible fluids in a porous media. In the case that the fluids have equal viscosity and the interface is graphical, this system reduces to a single nonlinear, nonlocal parabolic equation for

Get Price2010-6-16 In this paper we establish the structure of the mixing zone, and reveal a critical mechanism that plays a role in the growth of the leading edge of the mixing zone. It turns out that there is a close link between the growth rate of the mixing zone and a shape selection problem for Saffman–Taylor fingers.

Get Price2021-11-12 Gradient estimates for the insulated conductivity problem. Zhuolun Yang, Brown University. 9-27-2021 - 4:00PM (EDT) (joint with LCDS seminar), in-person, Rm 108, 170 Hope St. Abstract. We discuss the insulated conductivity problem with multiple inclusions embedded in a bounded domain in n-dimensional Euclidean space.

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Get Price2021-11-6 The domain of analyticity of solutions to the three-dimensional Euler equations in a half space. Discrete and Continuous Dynamical Systems 29 (2011), no. 1, 285-303. Igor Kukavica, Roger Temam, Vlad Vicol, Mohammed Ziane. Existence and uniqueness of solutions for the hydrostatic Euler equations on a bounded domain with analytic data.

Get Price2006-11-3 Solutions for Assays. The quantities given are sufficient for a class of about 100 students and can be scaled up or down as required. Appropriate aliquots of the solutions are supplied to each student. Analytical grade reagents should be used. All solutions

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