Local well-posedness for the fifth-order KdV equations on \(\mathbb{T}\)

DOI10.1016/j.jde.2016.02.001zbMath1339.35271arXiv1510.01017OpenAlexW2619132393MaRDI QIDQ264489

Chulkwang Kwak

Publication date: 31 March 2016

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

Full work available at URL: https://arxiv.org/abs/1510.01017

zbMATH Keywords

energy methodlocal well-posednesscomplete integrabilityfifth-order KdV equation\(X^{s, b}\) spacemodified energy

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53)

Related Items (10)

Low regularity well-posedness for generalized Benjamin–Ono equations on the circle ⋮ On short-time bilinear Strichartz estimates and applications to the Shrira equation ⋮ Global solutions and stability properties of the 5th order Gardner equation ⋮ Control and stabilization of the periodic fifth order Korteweg-de Vries equation ⋮ Low regularity Cauchy problem for the fifth-order modified KdV equations on 𝕋 ⋮ The initial-boundary value problem for the Kawahara equation on the half-line ⋮ Traveling wave solutions of space-time fractional generalized fifth-order KdV equation ⋮ Existence of solitary wave solutions for a nonlinear fifth-order KdV equation ⋮ Well-posedness issues on the periodic modified Kawahara equation ⋮ Numerical algorithm for time-fractional Sawada-Kotera equation and Itô equation with Bernstein polynomials

Cites Work

• Local well-posedness for dispersion generalized Benjamin-Ono equations in Sobolev spaces
• Lax pairs and higher order models for water waves
• Global well-posedness of the KP-I initial-value problem in the energy space
• On the fifth-order KdV equation: Local well-posedness and lack of uniform continuity of the solution map
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I: Schrödinger equations
• Rough solutions of the fifth-order KdV equations
• Multilinear weighted convolution of L 2 functions, and applications to nonlinear dispersive equations
• A bilinear estimate with applications to the KdV equation
• Low regularity Cauchy problem for the fifth-order modified KdV equations on 𝕋
• Well-posedness for the fifth-order KdV equation in the energy space

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