Traveling wave solutions to the one-phase Muskat problem: existence and stability

DOI10.1007/s00205-023-01951-zarXiv2211.06286MaRDI QIDQ6182693

Ian Tice, Huy Quang Nguyen

Publication date: 25 January 2024

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2211.06286

zbMATH Keywords

Darcy lawfree boundarytraveling waveMuskat problem

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with fluid mechanics (35Q35) Stability in context of PDEs (35B35) Flows in porous media; filtration; seepage (76S05) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Other free boundary flows; Hele-Shaw flows (76D27) Traveling wave solutions (35C07)

Cites Work

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• Fourier Analysis and Nonlinear Partial Differential Equations
• Global existence, singular solutions, and ill-posedness for the Muskat problem
• A First Course in Sobolev Spaces
• On the regularity of the composition of diffeomorphisms
• Traveling Wave Solutions to the Multilayer Free Boundary Incompressible Navier--Stokes Equations
• Traveling Wave Solutions to the Free Boundary Incompressible Navier‐Stokes Equations
• Traveling wave solutions to the inclined or periodic free boundary incompressible Navier-Stokes equations

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