A remark on global well-posedness of the derivative nonlinear Schrödinger equation on the circle

DOI10.1016/J.CRMA.2015.06.015zbMath1323.35164arXiv1502.02261OpenAlexW2135425541MaRDI QIDQ496078

Tadahiro Oh, Răzvan O. Moşincat

Publication date: 16 September 2015

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1502.02261

zbMATH Keywords

derivative nonlinear Schrödinger equationglobal well-posednesscompletely integrable

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15)

Related Items (11)

Gibbs measures associated to the integrals of motion of the periodic derivative nonlinear Schrödinger equation ⋮ Optimal small data scattering for the generalized derivative nonlinear Schrödinger equations ⋮ On the well-posedness problem for the derivative nonlinear Schrödinger equation ⋮ Growth bound and nonlinear smoothing for the periodic derivative nonlinear Schrödinger equation ⋮ Instability of solitary wave solutions for the nonlinear Schrödinger equation of derivative type in degenerate case ⋮ Global well-posedness of the derivative nonlinear Schrödinger equation with periodic boundary condition in \(H^{\frac{1}{2}}\) ⋮ Optimal local well-posedness for the periodic derivative nonlinear Schrödinger equation ⋮ Random data Cauchy problem for the nonlinear Schrödinger equation with derivative nonlinearity ⋮ On a priori estimates and existence of periodic solutions to the modified Benjamin-Ono equation below \(H^{1 / 2}(\mathbb{T})\) ⋮ Invariant measures for the periodic derivative nonlinear Schrödinger equation ⋮ Long-period limit of exact periodic traveling wave solutions for the derivative nonlinear Schrödinger equation

Cites Work

• Invariant weighted Wiener measures and almost sure global well-posedness for the periodic derivative NLS
• Nonlinear Schrödinger equations and sharp interpolation estimates
• Sharp Gagliardo-Nirenberg inequalities and mass transport theory
• Statistical mechanics of the nonlinear Schrödinger equation
• Blow-up solutions for mixed nonlinear Schrödinger equations
• Global well-posedness for the nonlinear Schrödinger equation with derivative in energy space
• Global Well-Posedness for Schrödinger Equations with Derivative
• Global Well-Posedness of the Derivative Nonlinear Schroedinger Equations on T
• Finite Energy Solutions of Nonlinear Schrödinger Equations of Derivative Type
• A Refined Global Well-Posedness Result for Schrödinger Equations with Derivative
• On the Cauchy problem for the derivative nonlinear Schrodinger equation with periodic boundary condition

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