On the well-posedness of incompressible flow in porous media with supercritical diffusion

DOI10.1080/00036810902913821zbMath1166.76054OpenAlexW1976213538WikidataQ58280225 ScholiaQ58280225MaRDI QIDQ5190737

Liutang Xue

Publication date: 27 July 2009

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00036810902913821

zbMATH Keywords

Besov spaceblowup criterionDarcy model

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Flows in porous media; filtration; seepage (76S05)

Related Items (5)

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 ⋮ Global existence of quasi-stratified solutions for the confined IPM equation ⋮ Global well‐posedness of the aggregation equation with supercritical dissipation in Besov spaces ⋮ Global well-posedness of the 3D incompressible porous media equation with critical dissipation in Triebel-Lizorkin spaces

Cites Work

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• Existence and uniqueness of the solution to the dissipative 2D quasi-geostrophic equations in the Sobolev space
• Global well-posedness for the critical 2D dissipative quasi-geostrophic equation
• A maximum principle applied to quasi-geostrophic equations
• Global solutions of the super-critical 2D quasi-geostrophic equation in Besov spaces
• A new Bernstein's inequality and the 2D dissipative quasi-geostrophic equation
• Analytical behavior of two-dimensional incompressible flow in porous media
• Density-dependent incompressible viscous fluids in critical spaces

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