Well-posedness of a kind of the free surface equation of shallow water waves

DOI10.1216/rmj.2020.50.1409zbMath1450.35121arXiv1901.01380OpenAlexW3091053869MaRDI QIDQ2204755

Zhouyu Li, Miaomiao Dang

Publication date: 16 October 2020

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1901.01380

zbMATH Keywords

local well-posednessone space dimensionwave-breaking

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Initial value problems for nonlinear higher-order PDEs (35G25) Strong solutions to PDEs (35D35)

Cites Work

• Unnamed Item
• On the Cauchy problem for the two-component Camassa-Holm system
• The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations
• On the global existence and wave-breaking criteria for the two-component Camassa-Holm system
• Wave breaking for nonlinear nonlocal shallow water equations
• A few remarks on the Camassa-Holm equation.
• Large time existence for 3D water waves and asymptotics
• A nonlocal shallow-water model arising from the full water waves with the Coriolis effect
• Vorticity and Incompressible Flow
• Nonhomogeneous Viscous Incompressible Fluids: Existence of Velocity, Density, and Pressure
• Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids
• A derivation of equations for wave propagation in water of variable depth
• A Nash-Moser theorem for singular evolution equations. Application to the Serre and Green-Naghdi equations
• A shallow‐water approximation to the full water wave problem