Large data local solutions for the derivative NLS equation

DOI10.4171/JEMS/136zbMath1250.35160arXivmath/0610092OpenAlexW2057916146MaRDI QIDQ952511

Ioan Bejenaru, Daniel Tataru

Publication date: 12 November 2008

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0610092

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30)

Related Items (14)

Local well-posedness of the Landau–Lifshitz equation with helicity term ⋮ Global wellposedness in the energy space for the Maxwell-Schrödinger system ⋮ Klein-Gordon-Schrödinger system: Dinucleon field ⋮ Quasilinear Schrödinger equations. I: Small data and quadratic interactions ⋮ Almost sure local well-posedness and scattering for the 4D cubic nonlinear Schrödinger equation ⋮ Well-posedness and smoothing effect for generalized nonlinear Schrödinger equations ⋮ Quasilinear Schrödinger equations. II: Small data and cubic nonlinearities ⋮ Wave packet parametrices for evolutions governed by pdo's with rough symbols ⋮ Near soliton evolution for equivariant Schroedinger Maps in two spatial dimensions ⋮ Quasilinear Schrödinger equations. III: Large data and short time. ⋮ Global Well-Posedness and Scattering for Derivative Schrödinger Equation ⋮ Large data local well-posedness for a class of KdV-type equations ⋮ A remark on the well-posedness for a system of quadratic derivative nonlinear Schrödinger equations ⋮ Global well-posedness and scattering for the derivative nonlinear Schrödinger equation with small rough data

Cites Work

• Unnamed Item
• Unnamed Item
• On first-order perturbations of the Schrödinger equation with conjugation.
• Smoothing effects and local existence theory for the generalized nonlinear Schrödinger equations
• Partial differential equations. 2: Qualitative studies of linear equations
• Gain of regularity for semilinear Schrödinger equations
• On the \(L^p\) norm of spectral clusters for compact manifolds with boundary
• Quadratic nonlinear derivative Schrodinger equations. Part I
• Quadratic nonlinear derivative Schrödinger equations - Part 2
• Resonance and long time existence for the quadratic semilinear schrödinger equation
• Dispersive estimates for principally normal pseudodifferential operators
• On the Cauchy-problem for generalized Kadomtsev-Petviashvili-II equations

This page was built for publication: Large data local solutions for the derivative NLS equation