Well-posedness of KdV with higher dispersion
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Publication:1038142
DOI10.1016/j.matcom.2009.06.007zbMath1179.35284OpenAlexW2087458597MaRDI QIDQ1038142
A. Alexandrou Himonas, Jennifer Gorsky
Publication date: 17 November 2009
Published in: Mathematics and Computers in Simulation (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.matcom.2009.06.007
KdV equations (Korteweg-de Vries equations) (35Q53) Critical exponents in context of PDEs (35B33) Existence problems for PDEs: global existence, local existence, non-existence (35A01)
Related Items (20)
Global well-posedness and nonsqueezing property for the higher-order KdV-type flow ⋮ On the control issues for higher-order nonlinear dispersive equations on the circle ⋮ On persistence of spatial analyticity for the dispersion-generalized periodic KdV equation ⋮ Local well-posedness for the periodic higher order KdV type equations ⋮ Global controllability and stabilizability of Kawahara equation on a periodic domain ⋮ The IVP for a periodic generalized ZK equation ⋮ A higher dispersion KdV equation on the line ⋮ Error estimate for a fully discrete spectral scheme for Korteweg-de Vries-Kawahara equation ⋮ Global smoothing for the periodic Benjamin equation in low-regularity spaces ⋮ Boundary smoothing properties of the Kawahara equation posed on the finite domain ⋮ Well-posedness and ill-posedness of KdV equation with higher dispersion ⋮ Local well-posedness for the dispersion generalized periodic KdV equation ⋮ The Cauchy problem of a periodic higher order KdV equation in analytic Gevrey spaces ⋮ Unnamed Item ⋮ The modified KdV equation with higher dispersion in Sobolev and analytic spaces on the line ⋮ Well-posedness issues on the periodic modified Kawahara equation ⋮ Remark on the persistence of spatial analyticity for cubic nonlinear Schrödinger equation on the circle ⋮ Asymptotic lower bound for the radius of spatial analyticity to solutions of KdV equation ⋮ Local well-posedness for periodic Benjamin equation with small initial data ⋮ Non-homogeneous boundary value problems of the Kawahara equation posed on a finite interval
Cites Work
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- Existence and uniqueness of solutions for the generalized Korteweg-de Vries equation
- Gain of regularity for equations of KdV type
- Remarks on the Korteweg-de Vries equation
- Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II: The KdV-equation
- Well-posedness of the Cauchy problem for a shallow water equation on the circle
- On the Korteweg - de Vries equation: Existence and uniqueness
- The initial-value problem for the Korteweg-de Vries equation
- 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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