Continuity properties of the data-to-solution map for the generalized Camassa-Holm equation

DOI10.1016/j.jmaa.2014.03.033zbMath1304.35610OpenAlexW1969752636MaRDI QIDQ483011

Yong-Cai Geng, Sumit K. Garg

Publication date: 15 December 2014

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

Full work available at URL: https://doi.org/10.1016/j.jmaa.2014.03.033

zbMATH Keywords

Fourier transformSobolev spacesCauchy problemHölder continuitypeakon solutionsCamassa-Holm equationDegasperis-Procesi equationintegrable equationscommutator estimatemultiplier estimatesNovikov equations

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Time series analysis of dynamical systems (37M10) Soliton solutions (35C08)

Related Items (11)

Well-posedness of the Fornberg-Whitham equation on the circle ⋮ On the Cauchy problem for a class of shallow water wave equations with \((k+1)\)-order nonlinearities ⋮ Nonuniform Dependence on Initial Data for Compressible Gas Dynamics: The Cauchy Problem on $\mathbb{R}^2$ ⋮ Global solutions for the generalized Camassa-Holm equation ⋮ Continuity properties of the data-to-solution map for the two-component higher order Camassa-Holm system ⋮ Well-posedness of the modified Camassa-Holm equation in Besov spaces ⋮ Blow-up phenomena and peakons for the gFQXL/gCH-mCH equation ⋮ Non-uniform dependence of the data-to-solution map for the Hunter-Saxton equation in Besov spaces ⋮ Conserved quantities, global existence and blow-up for a generalized CH equation ⋮ Persistent decay of solutions to the \(k- abc\) equation in weighted \(L^p\) spaces ⋮ Global existence and long time behavior of the generalized Camassa–Holm equation with k + 1 degree nonlinearities

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