Well posedness for a higher order modified Camassa-Holm equation

DOI10.1016/j.jde.2008.12.001zbMath1170.35087OpenAlexW2022539872MaRDI QIDQ1018399

Erika A. Olson

Publication date: 19 May 2009

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

Full work available at URL: https://doi.org/10.1016/j.jde.2008.12.001

zbMATH Keywords

Sobolev spacesCauchy problemharmonic analysiswell posednessnonlinear dispersive equationsbilinear estimatesmodified Camassa-Holm equation

Mathematics Subject Classification ID

Related Items (9)

Attractor for a viscous coupled Camassa-Holm equation ⋮ Well-posedness of a higher order modified Camassa-Holm equation in spaces of low regularity ⋮ Well-posedness for the stochastic higher order modified Camassa-Holm equation ⋮ The Cauchy problem for a fifth-order dispersive equation ⋮ On the generalized nonlinear Camassa-Holm equation ⋮ The local well-posedness and existence of weak solutions for a generalized Camassa-Holm equation ⋮ Uniformly random attractor for the three-dimensional stochastic nonautonomous Camassa-Holm equations ⋮ 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

Cites Work

• Global well-posedness of the Cauchy problem of the fifth-order shallow water equation
• Symplectic structures, their Bäcklund transformations and hereditary symmetries
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II: The KdV-equation
• The Cauchy problem for the Korteweg-de Vries equation in Sobolev spaces of negative indices
• On the Cauchy problem for periodic KdV-type equations
• The Cauchy problem for a fifth order evolution equation
• Well-posedness of the Cauchy problem for a shallow water equation on the circle
• Higher-Order Nonlinear Dispersive Equations
• The cauchy problem for a shallow water type equation
• An integrable shallow water equation with peaked solitons
• Sharp global well-posedness for KdV and modified KdV on ℝ and 𝕋
• A bilinear estimate with applications to the KdV equation

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