Well-posedness of a higher order modified Camassa-Holm equation in spaces of low regularity

DOI10.1007/s00028-010-0057-zzbMath1239.35141OpenAlexW2049276364MaRDI QIDQ423418

Xingyu Yang, Wei Yan, Yongsheng Li

Publication date: 2 June 2012

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

Full work available at URL: https://doi.org/10.1007/s00028-010-0057-z

zbMATH Keywords

well-posednessbilinear estimatesFourier restriction norm methodmodified Camassa-Holm equation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30)

Related Items (9)

Gibbs measure for the higher order modified Camassa-Holm equation ⋮ Well-posedness for the stochastic higher order modified Camassa-Holm equation ⋮ The Cauchy problem for a fifth-order dispersive equation ⋮ The Cauchy problem for the seventh-order dispersive equation in Sobolev space ⋮ Well-posedness and ill-posedness of KdV equation with higher dispersion ⋮ The Cauchy problem for higher-order modified Camassa-Holm equations on the circle ⋮ The Cauchy problem for a higher order shallow water type equation on the circle ⋮ A trilinear estimate with application to the perturbed nonlinear Schrödinger equations with the Kerr law nonlinearity ⋮ Periodic stochastic high-order Degasperis–Procesi equation with cylindrical fBm

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Global well-posedness of the Cauchy problem of the fifth-order shallow water equation
• Global conservative solutions of the Camassa-Holm equation
• The global attractor of the damped forced Ostrovsky equation
• Well posedness for a higher order modified Camassa-Holm equation
• Global well-posedness of Korteweg-de Vries equation in \(H^{-3/4}(\mathbb R)\)
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I: Schrödinger equations
• The Cauchy problem for the Korteweg-de Vries equation in Sobolev spaces of negative indices
• On the Cauchy problem for the Zakharov system
• Well-posedness of the Cauchy problem for a shallow water equation on the circle
• On the weak solutions to a shallow water equation
• Well-Posedness of the Initial Value Problem for the Korteweg-de Vries Equation
• The cauchy problem for a shallow water type equation
• Asymptotics, frequency modulation, and low regularity ill-posedness for canonical defocusing equations
• ON THE UNIQUENESS AND LARGE TIME BEHAVIOR OF THE WEAK SOLUTIONS TO A SHALLOW WATER EQUATION
• Sharp global well-posedness for KdV and modified KdV on ℝ and 𝕋
• A bilinear estimate with applications to the KdV equation

This page was built for publication: Well-posedness of a higher order modified Camassa-Holm equation in spaces of low regularity