[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 …
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 …
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 …
[HTML][HTML] Well-posedness of the Muskat problem with H2 initial data
CHA Cheng, R Granero-Belinchón, S Shkoller - Advances in Mathematics, 2016 - Elsevier
We study the dynamics of the interface between two incompressible fluids in a two-
dimensional porous medium whose flow is modeled by the Muskat equations. For the two …
dimensional porous medium whose flow is modeled by the Muskat equations. For the two …
The Muskat problem in two dimensions: equivalence of formulations, well-posedness, and regularity results
BV Matioc - Analysis & PDE, 2018 - msp.org
We consider the Muskat problem describing the motion of two unbounded immiscible fluid
layers with equal viscosities in vertical or horizontal two-dimensional geometries. We first …
layers with equal viscosities in vertical or horizontal two-dimensional geometries. We first …
Absence of splash singularities for surface quasi-geostrophic sharp fronts and the Muskat problem
In this paper, for both the sharp front surface quasi-geostrophic equation and the Muskat
problem, we rule out the “splash singularity” blow-up scenario; in other words, we prove that …
problem, we rule out the “splash singularity” blow-up scenario; in other words, we prove that …
Viscous displacement in porous media: the Muskat problem in 2D
BV Matioc - Transactions of the American Mathematical Society, 2018 - ams.org
We consider the Muskat problem describing the viscous displacement in a two-phase fluid
system located in an unbounded two-dimensional porous medium or Hele-Shaw cell. After …
system located in an unbounded two-dimensional porous medium or Hele-Shaw cell. After …
Well-posedness of the Muskat problem in subcritical Lp-Sobolev spaces
We study the Muskat problem describing the vertical motion of two immiscible fluids in a two-
dimensional homogeneous porous medium in an Lp-setting with p∈(1,∞). The Sobolev …
dimensional homogeneous porous medium in an Lp-setting with p∈(1,∞). The Sobolev …
Well-posedness for local and nonlocal quasilinear evolution equations in fluids and geometry
We establish a Schauder-type estimate for general local and non-local linear parabolic
system $$\partial_tu+\mathbf {L} _su=\Lambda^\gamma f+ g $$ in $(0,\infty)\times\mathbb …
system $$\partial_tu+\mathbf {L} _su=\Lambda^\gamma f+ g $$ in $(0,\infty)\times\mathbb …