Global existence and local well-posedness of the 2D viscous shallow water system in Sobolev spaces

DOI10.1080/00036811.2014.998205zbMath1348.35195OpenAlexW1985061527WikidataQ58258314 ScholiaQ58258314MaRDI QIDQ2795448

Zhaoyang Yin, Ya-nan Liu

Publication date: 21 March 2016

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

Full work available at URL: https://doi.org/10.1080/00036811.2014.998205

zbMATH Keywords

Sobolev spacesglobal existenceLittlewood-Paley theorylocal well-posedness2D viscous shallow water system

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Maximal functions, Littlewood-Paley theory (42B25) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03) Blow-up in context of PDEs (35B44) Besov spaces and (Q_p)-spaces (30H25)

Related Items (8)

The Herz-boundedness of commutators related to Schrödinger operators in the setting of Heisenberg group ⋮ Global well-posedness for the viscous shallow water system with Korteweg type ⋮ Ill-posedness issue for the 2D viscous shallow water equations in some critical Besov spaces ⋮ Finite-time blow-up of classical solutions to the rotating shallow water system with degenerate viscosity ⋮ Analytical properties for a stochastic rotating shallow water model under location uncertainty ⋮ Nonuniform dependence on initial data for the 2D viscous shallow water equations ⋮ Ill-posedness for the 2D viscous shallow water equations in the critical Besov spaces ⋮ Existence of strong solutions to the rotating shallow water equations with degenerate viscosities

Cites Work

• Global existence for the Cauchy problem for the viscous shallow water equations
• Existence of global weak solutions for a 2D viscous shallow water equations and convergence to the quasi-geostrophic model
• Global existence for the Dirichlet problem for the viscous shallow water equations
• The Cauchy problem for viscous shallow water equations
• On the Well-Posedness for the Viscous Shallow Water Equations
• Global Existence of Classical Solutions in the Dissipative Shallow Water Equations
• Existence and Uniqueness of a Classical Solution of an Initial-Boundary Value Problem of the Theory of Shallow Waters

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