Computer-assisted proofs in PDE: a survey
J Gómez-Serrano - SeMA Journal, 2019 - Springer
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[图书][B] Moving interfaces and quasilinear parabolic evolution equations
J Prüss, G Simonett - 2016 - Springer
Moving interfaces–and in the stationary case, free boundaries–are ubiquitous in our
environment and daily life. They are at the basis of many physical, chemical, and also …
environment and daily life. They are at the basis of many physical, chemical, and also …
[图书][B] Conformal and potential analysis in Hele-Shaw cells
B Gustafsson, A Vasil'ev - 2006 - books.google.com
This monograph presents recent and new ideas arising from the study of problems of planar
fluid dynamics, and which are interesting from the point of view of geometric function theory …
fluid dynamics, and which are interesting from the point of view of geometric function theory …
Rayleigh-Taylor breakdown for the Muskat problem with applications to water waves
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 …
porous media. The Rayleigh-Taylor condition is natural to reach linear stability of the Muskat …
Growth in the Muskat problem
R Granero-Belinchón, O Lazar - Mathematical Modelling of …, 2020 - mmnp-journal.org
Growth in the Muskat problem Page 1 Math. Model. Nat. Phenom. 15 (2020) 7 Mathematical
Modelling of Natural Phenomena https://doi.org/10.1051/mmnp/2019021 www.mmnp-journal.org …
Modelling of Natural Phenomena https://doi.org/10.1051/mmnp/2019021 www.mmnp-journal.org …
Interface evolution: the Hele-Shaw and Muskat problems
We study the dynamics of the interface between two incompressible 2-D flows where the
evolution equation is obtained from Darcy's law. The free boundary is given by the …
evolution equation is obtained from Darcy's law. The free boundary is given by the …
On the global existence for the Muskat problem.
The Muskat problem models the dynamics of the interface between two incompressible
immiscible fluids with different constant densities. In this work we prove three results. First …
immiscible fluids with different constant densities. In this work we prove three results. First …
A paradifferential approach for well-posedness of the Muskat problem
HQ Nguyen, B Pausader - Archive for Rational Mechanics and Analysis, 2020 - Springer
We study the Muskat problem for one fluid or two fluids, with or without viscosity jump, with or
without rigid boundaries, and in arbitrary space dimension d of the interface. The Muskat …
without rigid boundaries, and in arbitrary space dimension d of the interface. The Muskat …
Contour dynamics of incompressible 3-D fluids in a porous medium with different densities
We consider the problem of the evolution of the interface given by two incompressible fluids
through a porous medium, which is known as the Muskat problem and in two dimensions it …
through a porous medium, which is known as the Muskat problem and in two dimensions it …
Breakdown of smoothness for the Muskat problem
Á Castro, D Córdoba, C Fefferman… - Archive for Rational …, 2013 - Springer
Breakdown of Smoothness for the Muskat Problem Page 1 Digital Object Identifier (DOI)
10.1007/s00205-013-0616-x Arch. Rational Mech. Anal. 208 (2013) 805–909 Breakdown of …
10.1007/s00205-013-0616-x Arch. Rational Mech. Anal. 208 (2013) 805–909 Breakdown of …