A paradifferential approach for well-posedness of the Muskat problem
From MaRDI portal
Publication:2180913
DOI10.1007/s00205-020-01494-7zbMath1437.35588arXiv1907.03304OpenAlexW3101805917MaRDI QIDQ2180913
Benoit Pausader, Huy Quang Nguyen
Publication date: 15 May 2020
Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1907.03304
Smoothness and regularity of solutions to PDEs (35B65) PDEs in connection with fluid mechanics (35Q35) Flows in porous media; filtration; seepage (76S05)
Related Items
Refined Rellich boundary inequalities for the derivatives of a harmonic function ⋮ 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 multiphase Muskat problem with equal viscosities in two dimensions ⋮ Well-posedness of the Muskat problem in subcritical Lp-Sobolev spaces ⋮ The Muskat problem with 𝐶¹ data ⋮ A truncated real interpolation method and characterizations of screened Sobolev spaces ⋮ The vanishing surface tension limit of the Muskat problem ⋮ Global well-posedness for the three dimensional Muskat problem in the critical Sobolev space ⋮ Coercivity of the Dirichlet-to-Neumann operator and applications to the Muskat problem ⋮ Global existence in the Lipschitz class for the N-Peskin problem ⋮ 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 ⋮ Functional inequalities and strong Lyapunov functionals for free surface flows in fluid dynamics ⋮ Endpoint Sobolev theory for the Muskat equation ⋮ Critical local well‐posedness for the fully nonlinear Peskin problem ⋮ Regularity for a special case of two-phase Hele-Shaw flow via parabolic integro-differential equations ⋮ Traveling wave solutions to the one-phase Muskat problem: existence and stability ⋮ Global Regularity for Gravity Unstable Muskat Bubbles ⋮ Regularity of solutions to the Muskat equation ⋮ On an Asymptotic Model for Free Boundary Darcy Flow in Porous Media ⋮ Surface tension stabilization of the Rayleigh-Taylor instability for a fluid layer in a porous medium ⋮ On well-posedness of the Muskat problem with surface tension ⋮ On the Cauchy problem for the Muskat equation. II: Critical initial data ⋮ Mixing solutions for the Muskat problem with variable speed ⋮ Convexity and the Hele-Shaw equation ⋮ Global solutions for the Muskat problem in the scaling invariant Besov space \(\dot{B}_{\infty , 1}^1\) ⋮ On the Cauchy problem for the Muskat equation with non-Lipschitz initial data ⋮ 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
- Unnamed Item
- Strichartz estimates and local existence for the gravity-capillary waves with non-Lipschitz initial velocity
- ``Graph paper trace characterizations of functions of finite energy
- Porous media: The Muskat problem in three dimensions
- Local solvability and turning for the inhomogeneous Muskat problem
- Rayleigh-Taylor breakdown for the Muskat problem with applications to water waves
- On the Cauchy problem for gravity water waves
- Two dimensional water waves in holomorphic coordinates
- On the parabolicity of the Muskat problem: Well-posedness, fingering, and stability results
- On the water-wave equations with surface tension
- Interface evolution: the Hele-Shaw and Muskat problems
- The Hele--Shaw problem and area-preserving curve-shortening motions
- The confined Muskat problem: differences with the deep water regime
- A maximum principle for the Muskat problem for fluids with different densities
- Dynamics near unstable, interfacial fluids
- Well-posedness of the Muskat problem with \(H^2\) initial data
- Para-differential calculus and applications to the Cauchy problem for nonlinear systems
- Lectures on nonlinear hyperbolic differential equations
- Well-posedness in Sobolev spaces of the full water wave problem in 2D
- Classical solutions for Hele-Shaw models with surface tension
- 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
- A sharp Cauchy theory for the 2D gravity-capillary waves
- A survey for the Muskat problem and a new estimate
- On the Muskat problem with viscosity jump: global in time results
- A priori estimates for water waves with emerging bottom
- On the global existence for the Muskat problem
- On well-posedness of the Muskat problem with surface tension
- Paralinearization of the Muskat equation and application to the Cauchy problem
- Lyapunov functions, identities and the Cauchy problem for the Hele-Shaw equation
- Low regularity solutions for gravity water waves
- Some free boundary problems recast as nonlocal parabolic equations
- Traces for homogeneous Sobolev spaces in infinite strip-like domains
- On the local and global existence of solutions to 1d transport equations with nonlocal velocity
- 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
- The vanishing surface tension limit of the Muskat problem
- On the Muskat problem: Global in time results in 2D and 3D
- Fourier Analysis and Nonlinear Partial Differential Equations
- Global existence, singular solutions, and ill-posedness for the Muskat problem
- The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid
- Paralinearization of the Dirichlet to Neumann Operator, and Regularity of Three-Dimensional Water Waves
- Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires
- Well-posedness in Sobolev spaces of the full water wave problem in 3-D
- Viscous displacement in porous media: the Muskat problem in 2D
- A Paradifferential Reduction for the Gravity-capillary Waves System at Low Regularity and Applications
- Well-posedness of two-phase Hele–Shaw flow without surface tension
- Well-posedness of the water-waves equations
- On turning waves for the inhomogeneous Muskat problem: a computer-assisted proof
- Well-posedness and decay to equilibrium for the Muskat problem with discontinuous permeability
- Local-existence for the inhomogeneous Muskat problem
- On the Two‐Dimensional Muskat Problem with Monotone Large Initial Data
- Global solutions for small data to the Hele-Shaw problem
- Strichartz Estimates and the Cauchy Problem for the Gravity Water Waves Equations
- Well-posedness of two-phase Darcy flow in 3D
- Global Existence for the Confined Muskat Problem