Well-posedness and wave breaking for a shallow water wave model with large amplitude

DOI10.1007/S00028-019-00518-4zbMath1439.35414OpenAlexW2947487289WikidataQ127803707 ScholiaQ127803707MaRDI QIDQ1987647

Shouming Zhou

Publication date: 15 April 2020

Published in: Journal of Evolution Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00028-019-00518-4

zbMATH Keywords

well-posednessBesov spaceswave breakingshallow water waves of large amplitude

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with fluid mechanics (35Q35) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Maximal functions, Littlewood-Paley theory (42B25) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Wave equation (35L05) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Blow-up in context of PDEs (35B44) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Strong solutions to PDEs (35D35)

Related Items (4)

Well-posedness of a highly nonlinear shallow water equation on the circle ⋮ A highly nonlinear shallow-water model Arising from the full water waves with the Coriolis effect ⋮ The highly nonlinear shallow water equation: local well-posedness, wave breaking data and non-existence of \(sech^2\) solutions ⋮ Symmetric waves are traveling waves of some shallow water scalar equations

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