On the well-posedness of a mathematical model describing water-mud interaction

DOI10.1002/mma.2692zbMath1273.35085arXiv1202.2965OpenAlexW2094951486MaRDI QIDQ2846210

Joachim Escher, Anca-Voichita Matioc

Publication date: 5 September 2013

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1202.2965

zbMATH Keywords

classical solutionnon-Newtonian fluidtwo-phase moving boundary problem

Mathematics Subject Classification ID

Integral representations of solutions to PDEs (35C15) Boundary value problems for linear first-order PDEs (35F15)

Cites Work

• On the parabolicity of the Muskat problem: Well-posedness, fingering, and stability results
• On the two-phase Navier-Stokes equations with surface tension
• Interface evolution: the Hele-Shaw and Muskat problems
• A moving boundary problem for periodic Stokesian Hele-Shaw flows
• Existence of weak solutions for a diffuse interface model for viscous, incompressible fluids with general densities
• Equations d'évolution abstraites non linéaires de type parabolique
• First-Order System Least Squares for Coupled Stokes–Darcy Flow
• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I
• $L_p$-Theory for a Class of Non-Newtonian Fluids
• Analytic semigroups and optimal regularity in parabolic problems
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