On sharp global well-posedness and ill-posedness for a fifth-order KdV-BBM type equation

DOI10.1016/j.jmaa.2019.06.045zbMath1426.35199arXiv1805.06039OpenAlexW2964351369MaRDI QIDQ2320101

Xavier Carvajal, Mahendra Panthee

Publication date: 21 August 2019

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1805.06039

zbMATH Keywords

BBM equationKdV equationCauchy problemslocal \& global well-posednessnonlinear dispersive wave equationswater wave models

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) KdV equations (Korteweg-de Vries equations) (35Q53) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Ill-posed problems for PDEs (35R25) Existence problems for PDEs: global existence, local existence, non-existence (35A01)

Related Items

Construction of invariant solutions and conservation laws to the \((2+1)\)-dimensional integrable coupling of the KdV equation ⋮ Long-time asymptotics of a linear higher-order water wave model ⋮ On the well-posedness of higher order viscous Burgers' equations ⋮ On the well-posedness, ill-posedness and norm-inflation for a higher order water wave model on a periodic domain ⋮ Lower bound on the radius of analyticity of solution for fifth order KdV-BBM equation ⋮ On propagation of regularities and evolution of radius of analyticity in the solution of the fifth-order KdV-BBM model

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Well-posedness of a model for water waves with viscosity
• On the ill-posedness result for the BBM equation
• Sharp well-posedness and ill-posedness results for a quadratic nonlinear Schrödinger equation
• The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations
• Sharp well-posedness results for the BBM equation
• Periodic Korteweg-de Vries equation with measures as initial data
• On asymptotically equivalent shallow water wave equations
• Higher-order Hamiltonian model for unidirectional water waves
• Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media. I: Derivation and linear theory
• Well-posedness for a higher-order, nonlinear, dispersive equation on a quarter plane
• DECOUPLED AND UNIDIRECTIONAL ASYMPTOTIC MODELS FOR THE PROPAGATION OF INTERNAL WAVES
• Sharp ill-posedness and well-posedness results for the KdV-Burgers equation: the real line case
• Hamiltonian perturbation theory and water waves
• The initial-value problem for the Korteweg-de Vries equation
• Global well-posedness for the modified korteweg-de vries equation
• Camassa–Holm, Korteweg–de Vries-5 and other asymptotically equivalent equations for shallow water waves
• Global existence for the critical generalized KdV equation
• Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media: II. The nonlinear theory
• Global solutions and ill-posedness for the Kaup system and related Boussinesq systems
• On ill-posedness of truncated series models for water waves