On the Cauchy problem for the Muskat equation. II: Critical initial data
From MaRDI portal
Publication:2040260
DOI10.1007/s40818-021-00099-xzbMath1473.35430arXiv2009.08442OpenAlexW3147711979MaRDI QIDQ2040260
Publication date: 12 July 2021
Published in: Annals of PDE (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2009.08442
PDEs in connection with fluid mechanics (35Q35) Flows in porous media; filtration; seepage (76S05) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Liquid-liquid two component flows (76T06)
Related Items
A note on the dissipation for the general Muskat problem ⋮ On the dynamics of the roots of polynomials under differentiation ⋮ Localized mixing zone for Muskat bubbles and turned interfaces ⋮ The Muskat problem with 𝐶¹ data ⋮ Global well-posedness for the three dimensional Muskat problem in the critical Sobolev space ⋮ Global existence and decay of the inhomogeneous Muskat problem with Lipschitz initial data ⋮ Global well‐posedness for the one‐phase Muskat problem ⋮ The Peskin Problem with \({\boldsymbol{\dot B^1_{\infty,\infty }}}\) Initial Data ⋮ Endpoint Sobolev theory for the Muskat equation ⋮ Critical local well‐posedness for the fully nonlinear Peskin problem ⋮ Regularity of solutions to the Muskat equation ⋮ Rigidity of acute angled corners for one phase Muskat interfaces ⋮ Quasilinearization of the 3D Muskat equation, and applications to the critical Cauchy problem ⋮ Self-similar solutions for the Muskat equation
Cites Work
- Unnamed Item
- Splash singularities for the one-phase Muskat problem in stable regimes
- Rayleigh-Taylor breakdown for the Muskat problem with applications to water waves
- Interface evolution: the Hele-Shaw and Muskat problems
- A maximum principle for the Muskat problem for fluids with different densities
- Well-posedness of the Muskat problem with \(H^2\) initial data
- Characterizations of Besov-Hardy-Sobolev spaces: A unified approach
- Classical solutions for Hele-Shaw models with surface tension
- Global classical solution of Muskat free boundary problem.
- The Muskat problem in two dimensions: equivalence of formulations, well-posedness, and regularity results
- Global well-posedness for the two-dimensional Muskat problem with slope less than 1
- On the Muskat problem with viscosity jump: global in time results
- On the global existence for the Muskat problem
- On the Sobolev space of functions with derivative of logarithmic order
- A paradifferential approach for well-posedness of the Muskat problem
- Paralinearization of the Muskat equation and application to the Cauchy problem
- Global regularity for 2D Muskat equations with finite slope
- Contour dynamics of incompressible 3-D fluids in a porous medium with different densities
- Breakdown of smoothness for the Muskat problem
- Moving Interfaces and Quasilinear Parabolic Evolution Equations
- On the Muskat problem: Global in time results in 2D and 3D
- Global existence, singular solutions, and ill-posedness for the Muskat problem
- A Localized Approximation Method for Vortical Flows
- Large time decay estimates for the Muskat equation
- Well-posedness of two-phase Hele–Shaw flow without surface tension
- On an Asymptotic Model for Free Boundary Darcy Flow in Porous Media
- On the Two‐Dimensional Muskat Problem with Monotone Large Initial Data
- Well-posedness of two-phase Darcy flow in 3D
This page was built for publication: On the Cauchy problem for the Muskat equation. II: Critical initial data
