Analytical behavior of two-dimensional incompressible flow in porous media

DOI10.1063/1.2404593zbMath1144.81332OpenAlexW1974569132MaRDI QIDQ3529767

Diego Cordoba, Rafael Orive-Illera, Francisco Gancedo

Publication date: 14 October 2008

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://idus.us.es/handle/11441/45315

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) PDEs in connection with fluid mechanics (35Q35) Flows in porous media; filtration; seepage (76S05) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03)

Related Items (23)

Hölder continuous solutions of active scalar equations ⋮ On the second iterate for critically diffusive active scalar equations ⋮ Analyticity of Lagrangian trajectories for well posed inviscid incompressible fluid models ⋮ Small scale formations in the incompressible porous media equation ⋮ On the regularity of the solution map of the incompressible porous media equation ⋮ The Toda flow as a porous medium equation ⋮ The generalized Buckley-Leverett system: solvability ⋮ On the well-posedness of the incompressible porous media equation in Triebel-Lizorkin spaces ⋮ Global existence of quasi-stratified solutions for the confined IPM equation ⋮ A note on interface dynamics for convection in porous media ⋮ Regularity of Hölder continuous solutions of the supercritical porous media equation ⋮ Fractional Schrödinger dynamics and decoherence ⋮ Wellposedness and convergence of solutions to a class of forced non-diffusive equations with applications ⋮ Remarks on a paper by Gavrilov: Grad-Shafranov equations, steady solutions of the three dimensional incompressible Euler equations with compactly supported velocities, and applications ⋮ On the well-posedness of incompressible flow in porous media with supercritical diffusion ⋮ Lack of uniqueness for weak solutions of the incompressible porous media equation ⋮ Vanishing diffusion limits and long time behaviour of a class of forced active scalar equations ⋮ Absence of squirt singularities for the multi-phase Muskat problem ⋮ Global well-posedness of the 3D incompressible porous media equation with critical dissipation in Triebel-Lizorkin spaces ⋮ 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 ⋮ Fluid dynamics on logarithmic lattices ⋮ On a singular incompressible porous media equation

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• Small-scale structures in Boussinesq convection
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