Well-posedness and derivative blow-up for a dispersionless regularized shallow water system

DOI10.1088/1361-6544/ab2cf1zbMath1428.35375arXiv1810.06096OpenAlexW3101158992MaRDI QIDQ5240841

Jian-Guo Liu, Robert L. Pego, Yue Pu

Publication date: 29 October 2019

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.06096

zbMATH Keywords

weak solutionslong wavesbreakdownSaint-Venant equationsGreen-Naghdi equationsnonlocal hyperbolic system

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Shocks and singularities for hyperbolic equations (35L67) PDEs in connection with fluid mechanics (35Q35) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Continuation and prolongation of solutions to PDEs (35B60) Blow-up in context of PDEs (35B44)

Related Items

Existence of Global Classical Solutions for the Saint-Venant Equations, On the blow-up scenario for some modified Serre-Green-Naghdi equations, Non-linear singularity formation for circular vortex sheets, On a Hamiltonian regularization of scalar conservation laws, Hamiltonian regularisation of the unidimensional barotropic Euler equations, Hamiltonian regularisation of shallow water equations with uneven bottom

Cites Work

• Unnamed Item
• Large time existence for 1D Green-Naghdi equations
• On an integrable two-component Camassa-Holm shallow water system
• Compressible fluid flow and systems of conservation laws in several space variables
• Global conservative solutions of the Camassa-Holm equation
• Global existence and blow-up phenomena for an integrable two-component Camassa-Holm shallow water system
• On the global existence and wave-breaking criteria for the two-component Camassa-Holm system
• Weakly singular shock profiles for a non-dispersive regularization of shallow-water equations
• On weakly singular and fully nonlinear travelling shallow capillary-gravity waves in the critical regime
• Non-dispersive conservative regularisation of nonlinear shallow water (and isentropic Euler equations)
• A two-component generalization of the Camassa-Holm equation and its solutions
• Two-component generalizations of the Camassa-Holm equation
• Variational derivation of two-component Camassa–Holm shallow water system
• GLOBAL DISSIPATIVE SOLUTIONS OF THE CAMASSA–HOLM EQUATION
• Extended Camassa-Holm Hierarchy and Conserved Quantities
• Commutator estimates and the euler and navier-stokes equations
• On the theory of water waves
• A derivation of equations for wave propagation in water of variable depth
• Global Solutions for the Two-Component Camassa–Holm System
• A new two-component system modelling shallow-water waves
• 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