The Muskat problem with 𝐶¹ data

2021 ◽  
Author(s):  
Ke Chen ◽  
Quoc-Hung Nguyen ◽  
Yiran Xu
Keyword(s):  
Muskat Problem

scholarly journals The Muskat problem with surface tension and equal viscosities in subcritical $$L_p$$-Sobolev spaces

2021 ◽  
Author(s):  
Anca-Voichita Matioc ◽  
Bogdan-Vasile Matioc
Keyword(s):  
Mathematical Model ◽  
Surface Tension ◽  
Global Existence ◽  
Sobolev Spaces ◽  
Existence Of Solutions ◽  
Well Posedness ◽  
Global Existence Of Solutions ◽  
Muskat Problem ◽  
The Mathematical Model ◽  
Quasilinear Parabolic

AbstractIn this paper we establish the well-posedness of the Muskat problem with surface tension and equal viscosities in the subcritical Sobolev spaces $$W^s_p(\mathbb {R})$$ W p s ( R ) , where $${p\in (1,2]}$$ p ∈ ( 1 , 2 ] and $${s\in (1+1/p,2)}$$ s ∈ ( 1 + 1 / p , 2 ) . This is achieved by showing that the mathematical model can be formulated as a quasilinear parabolic evolution problem in $$W^{\overline{s}-2}_p(\mathbb {R})$$ W p s ¯ - 2 ( R ) , where $${\overline{s}\in (1+1/p,s)}$$ s ¯ ∈ ( 1 + 1 / p , s ) . Moreover, we prove that the solutions become instantly smooth and we provide a criterion for the global existence of solutions.

scholarly journals On the Muskat problem: Global in time results in 2D and 3D

2016 ◽  
Vol 138 (6) ◽  
pp. 1455-1494 ◽  
Author(s):  
Peter Constantin ◽  
Diego Córdoba ◽  
Francisco Gancedo ◽  
Luis Rodríguez-Piazza ◽  
Robert M. Strain
Keyword(s):  
Muskat Problem ◽  
2D And 3D

scholarly journals The Muskat problem and related topics

2018 ◽  
Vol 58 (3) ◽  
pp. 284-308
Author(s):  
Anvarbek Meirmanov ◽  
Oleg Galtsev
Keyword(s):  
Muskat Problem

scholarly journals Mixing solutions for the Muskat problem with variable speed

2020 ◽  
Author(s):  
Florent Noisette ◽  
László Székelyhidi
Keyword(s):  
Weak Solutions ◽  
Variable Speed ◽  
Mixing Speed ◽  
Link Type ◽  
Muskat Problem ◽  
Quick Proof ◽  
Math Phys

AbstractWe 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).

scholarly journals Porous media: The Muskat problem in three dimensions

2013 ◽  
Vol 6 (2) ◽  
pp. 447-497 ◽  
Author(s):  
Antonio Córdoba ◽  
Diego Córdoba ◽  
Francisco Gancedo
Keyword(s):  
Porous Media ◽  
Three Dimensions ◽  
Muskat Problem

The Muskat problem with surface tension and a nonregular initial interface

2011 ◽  
Vol 74 (17) ◽  
pp. 6074-6096 ◽  
Author(s):  
Borys V. Bazaliy ◽  
Nataliya Vasylyeva
Keyword(s):  
Surface Tension ◽  
Muskat Problem
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