Energy solutions for the fifth-order modified Korteweg de-Vries equations
DOI10.3934/dcds.2024060zbMATH Open1546.35192MaRDI QIDQ6592956
Publication date: 26 August 2024
Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)
Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with fluid mechanics (35Q35) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Waves in compressible fluids (76N30)
Cites Work
- Title not available (Why is that?)
- Title not available (Why is that?)
- Local well-posedness for the fifth-order KdV equations on \(\mathbb{T}\)
- A note on ill posedness for the KdV equation.
- On the Korteweg-de Vries equation
- On the hierarchies of higher order mKdV and KdV equations
- Lax pairs and higher order models for water waves
- Local well-posedness in low regularity of the mKdV equation with periodic boundary condition
- Global wellposedness of KdV in \(H^{-1}(\mathbb T,\mathbb R)\)
- 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
- Remarks on the Korteweg-de Vries equation
- Solutions of the Korteweg-de Vries equation in fractional order Sobolev spaces
- Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II: The KdV-equation
- On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves.
- On the wellposedness of the KdV/KdV2 equations and their frequency maps
- Global well-posedness for the fifth-order KdV equation in \(H^{-1}(\mathbb{R})\)
- KdV is well-posed in \(H^{-1}\)
- On unconditional well-posedness for the periodic modified Korteweg-de Vries equation
- Rough solutions of the fifth-order KdV equations
- Multilinear weighted convolution of \(L^2\) functions, and applications to nonlinear dispersive equations
- Global well-posedness of the Benjamin–Ono equation in low-regularity spaces
- The initial-value problem for the Korteweg-de Vries equation
- A simple model of the integrable Hamiltonian equation
- Well‐posedness and scattering results for the generalized korteweg‐de vries equation via the contraction principle
- Higher-Order Nonlinear Dispersive Equations
- Method for Solving the Korteweg-deVries Equation
- Global Well-Posedness of mKdV inL2(𝕋, ℝ)
- Korteweg-de Vries Equation and Generalizations. I. A Remarkable Explicit Nonlinear Transformation
- Korteweg-de Vries Equation and Generalizations. II. Existence of Conservation Laws and Constants of Motion
- 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
- Three Lectures on “Fifty Years of KdV: An Integrable System”
- Low regularity Cauchy problem for the fifth-order modified KdV equations on 𝕋
- Well-posedness and ill-posedness of the fifth order modifed KdV equation
- Well-posedness for the fifth-order KdV equation in the energy space
- Integrals of nonlinear equations of evolution and solitary waves
This page was built for publication: Energy solutions for the fifth-order modified Korteweg de-Vries equations
Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6592956)
