Incompressible flow in porous media with fractional diffusion

DOI10.1088/0951-7715/22/8/002zbMath1169.76058arXiv0806.1180OpenAlexW3124900456MaRDI QIDQ3395280

Francisco Gancedo, Rafael Orive-Illera, Angel Castro, Diego Cordoba

Publication date: 25 August 2009

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0806.1180

zbMATH Keywords

uniquenessDarcy's lawattractorglobal existence

Mathematics Subject Classification ID

Related Items (28)

Inviscid limits for active scalar equations with mildly singular gradients ⋮ Non-uniqueness in law for the Boussinesq system forced by random noise ⋮ Local well-posedness for the quasi-geostrophic equations in Besov-Lorentz spaces ⋮ Structural stability for temperature-dependent bidispersive flow in a semi-infinite pipe ⋮ Global well‐posedness for incompressible flow in porous media with partial diffusion or fractional diffusion ⋮ Remarks on the method of modulus of continuity and the modified dissipative porous media equation ⋮ On the loss of continuity for super-critical drift-diffusion equations ⋮ On electroconvection in porous media ⋮ The Mathematical Theories of Diffusion: Nonlinear and Fractional Diffusion ⋮ Note on the well-posedness of a slightly supercritical surface quasi-geostrophic equation ⋮ On the regularity criteria of a surface quasi-geostrophic equation ⋮ Spatial-decay of solutions to the quasi-geostrophic equation with the critical and supercritical dissipation ⋮ On the Navier-Stokes equations in scaling-invariant spaces in any dimension ⋮ On the well-posedness of the quasi-geostrophic equation in the Triebel-Lizorkin-Lorentz spaces ⋮ Global existence for some transport equations with nonlocal velocity ⋮ On the well-posedness of the incompressible porous media equation in Triebel-Lizorkin spaces ⋮ On one multidimensional compressible nonlocal model of the dissipative QG equations ⋮ Continuous dependence on modelling for temperature-dependent bidispersive flow ⋮ Regularity of Hölder continuous solutions of the supercritical porous media equation ⋮ Nonlocal maximum principles for active scalars ⋮ Well-posedness of an asymptotic model for capillarity-driven free boundary Darcy flow in porous media in the critical Sobolev space ⋮ Suppression of blow up by a logistic source in 2D Keller-Segel system with fractional dissipation ⋮ Unique ergodicity for fractionally dissipated, stochastically forced 2D Euler equations ⋮ Global well-posedness of the 3D incompressible porous media equation with critical dissipation in Triebel-Lizorkin spaces ⋮ A local-in-time theory for singular SDEs with applications to fluid models with transport noise ⋮ Global well-posedness of incompressible flow in porous media with critical diffusion in Besov spaces ⋮ On the Regularity Issues of a Class of Drift-Diffusion Equations with Nonlocal Diffusion ⋮ On Moffatt's magnetic relaxation equations

This page was built for publication: Incompressible flow in porous media with fractional diffusion