Local well-posedness for the dispersion generalized periodic KdV equation

DOI10.1016/j.jmaa.2011.01.026zbMath1216.35117OpenAlexW2056127007MaRDI QIDQ531877

Junfeng Li, Shaoguang Shi

Publication date: 20 April 2011

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.2011.01.026

zbMATH Keywords

local well-posednessPicard iterationKorteweg de Vries (KdV) equation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Applications of operator theory to differential and integral equations (47N20) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (8)

On persistence of spatial analyticity for the dispersion-generalized periodic KdV equation ⋮ Global controllability and stabilizability of Kawahara equation on a periodic domain ⋮ A local well-posed result for the fifth order KP-II initial value problem ⋮ Global smoothing for the periodic Benjamin equation in low-regularity spaces ⋮ Boundary smoothing properties of the Kawahara equation posed on the finite domain ⋮ Stabilization of dispersion-generalized Benjamin-Ono ⋮ On the Cauchy problem for the fractional Camassa-Holm equation ⋮ Local well-posedness for periodic Benjamin equation with small initial data

Cites Work

• Global well-posedness and I method for the fifth order Korteweg-de Vries equation
• Global well-posedness of Korteweg-de Vries equation in \(H^{-3/4}(\mathbb R)\)
• Well-posedness of KdV with higher dispersion
• Low regularity solutions of two fifth-order KdV type equations
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II: The KdV-equation
• Multilinear estimates for periodic KdV equations, and applications
• Well-posedness of the Cauchy problem for a shallow water equation on the circle
• Asymptotics, frequency modulation, and low regularity ill-posedness for canonical defocusing equations
• Sharp global well-posedness for KdV and modified KdV on ℝ and 𝕋
• A bilinear estimate with applications to the KdV equation
• Remark on the local ill-posedness for KdV equation

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