Global well-posedness for the derivative nonlinear Schrödinger equation

DOI10.1007/s00222-022-01113-0zbMath1496.35350arXiv2012.01923OpenAlexW3110549300MaRDI QIDQ2152485

Hajer Bahouri, Galina Perelman

Publication date: 8 July 2022

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2012.01923

zbMATH Keywords

inverse scattering transformintegrable systemsderivative nonlinear Schrödinger equationglobal well-posednessBäcklund transformationprofile decompositions

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) NLS equations (nonlinear Schrödinger equations) (35Q55) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items

Well-posedness of the Cauchy problem for the kinetic DNLS on T, On the well-posedness problem for the derivative nonlinear Schrödinger equation, Refined probabilistic local well-posedness for a cubic Schrödinger half-wave equation, Quasi-invariance of low regularity Gaussian measures under the gauge map of the periodic derivative NLS, Remarks on blow-up criteria for the derivative nonlinear Schrödinger equation under the optimal threshold setting, A remark on the well-posedness for a system of quadratic derivative nonlinear Schrödinger equations, Stability of algebraic solitons for nonlinear Schrödinger equations of derivative type: variational approach, Global Cauchy problems for the nonlocal (derivative) NLS in \(E_\sigma^s\)

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