Well-posedness of two-phase Darcy flow in 3D

DOI10.1090/S0033-569X-07-01055-3zbMath1147.35073MaRDI QIDQ5424303

David M. Ambrose

Publication date: 5 November 2007

Published in: Quarterly of Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

Darcy's lawtwo-fluid flowlocal-in-time existence of solutions

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Multiphase and multicomponent flows (76T99)

Related Items

Global regularity for 2D Muskat equations with finite slope ⋮ The Muskat problem with 𝐶¹ data ⋮ A small-scale decomposition for 3D boundary integral computations with surface tension ⋮ The vanishing surface tension limit of the Muskat problem ⋮ A paradifferential approach for well-posedness of the Muskat problem ⋮ Global well‐posedness for the one‐phase Muskat problem ⋮ Endpoint Sobolev theory for the Muskat equation ⋮ A survey for the Muskat problem and a new estimate ⋮ A non-stiff boundary integral method for 3D porous media flow with surface tension ⋮ Well-posedness of a two-dimensional coordinate-free model for the motion of flame fronts ⋮ On the Muskat problem with viscosity jump: global in time results ⋮ Well-posedness of the Hele-Shaw-Cahn-Hilliard system ⋮ The zero surface tension limit of two-dimensional interfacial Darcy flow ⋮ On well-posedness of the Muskat problem with surface tension ⋮ The zero surface tension limit of three-dimensional interfacial Darcy flow ⋮ On the Cauchy problem for the Muskat equation. II: Critical initial data ⋮ 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 ⋮ Convergence of a boundary integral method for 3D interfacial Darcy flow with surface tension ⋮ Quasilinearization of the 3D Muskat equation, and applications to the critical Cauchy problem

Cites Work

• Unnamed Item
• Free boundary problems with surface tension conditions
• Removing the stiffness from interfacial flows with surface tension
• A center manifold analysis for the Mullins-Sekerka model
• Well-posedness of 3D vortex sheets with surface tension
• Vorticity and Incompressible Flow
• Global existence, singular solutions, and ill-posedness for the Muskat problem
• Time Dependent Free Boundary Problems
• The zero surface tension limit of three-dimensional water waves
• Well-posedness in Sobolev spaces of the full water wave problem in 3-D
• Lagrangian theory for 3D vortex sheets with axial or helical symmetry
• Classical Solutions of Multidimensional Hele--Shaw Models
• Well-Posedness of Vortex Sheets with Surface Tension
• A Free Boundary Problem for an Elliptic-Hyperbolic System: An Application to Tumor Growth
• Well-posedness of two-phase Hele–Shaw flow without surface tension
• Generalized vortex methods for free-surface flow problems
• Vortex Dynamics
• The long-time motion of vortex sheets with surface tension

This page was built for publication: Well-posedness of two-phase Darcy flow in 3D