Ill-posedness of Kawahara equation and Kaup-Kupershmidt equation

DOI10.1016/j.jmaa.2011.03.047zbMath1216.35127OpenAlexW1975171287MaRDI QIDQ536251

Wei Yan, Yongsheng Li

Publication date: 16 May 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.2011.03.047

zbMATH Keywords

ill-posednessKaup-Kupershmidt equationKawahara equationgeneral well-posedness principle

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Ill-posed problems for PDEs (35R25)

Related Items

Convergence problem of the Kawahara equation on the real line, Non-homogeneous initial-boundary-value problem of the fifth-order Korteweg-de Vries equation with a nonlinear dispersive term

Cites Work

• Unnamed Item
• Sharp well-posedness and ill-posedness results for a quadratic nonlinear Schrödinger equation
• Well-posedness and ill-posedness for a fifth-order shallow water wave equation
• Well-posedness for the fifth-order shallow water equations
• 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
• The Cauchy problem for the Korteweg-de Vries equation in Sobolev spaces of negative indices
• Periodic Korteweg-de Vries equation with measures as initial data
• Global existence of solutions for the Kawahara equation in Sobolev spaces of negative indices
• Global existence of solutions for the Cauchy problem of the Kawahara equation with \(L^2\) initial data
• The Cauchy problem for the fifth order shallow water equation
• Multilinear weighted convolution of L 2 functions, and applications to nonlinear dispersive equations
• The Cauchy problem for Kawahara equation in Sobolev spaces with low regularity
• On the Inverse Scattering Problem for Cubic Eigenvalue Problems of the Class ψ_xxx + 6Qψ_x + 6R_ψ = λψ
• Existence and Nonexistence of Solitary Wave Solutions to Higher-Order Model Evolution Equations
• A model for the two-way propagation of water waves in a channel
• 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