Quasilinear Schrödinger equations. II: Small data and cubic nonlinearities

DOI10.1215/21562261-2693424zbMath1309.35140arXiv1208.0544OpenAlexW1984035585MaRDI QIDQ2258608

Jeremy L. Marzuola, Jason Metcalfe, Daniel Tataru

Publication date: 26 February 2015

Published in: Kyoto Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1208.0544

zbMATH Keywords

quasilinear Schrödinger equationsMizohata's integrability condition

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) Existence problems for PDEs: global existence, local existence, non-existence (35A01)

Related Items (11)

Local well-posedness for quasi-linear problems: A primer ⋮ The dual approach to stationary and evolution quasilinear PDEs ⋮ Global transversal stability of Euclidean planes under skew mean curvature flow evolutions ⋮ Local well-posedness of the skew mean curvature flow for small data in \(d \geqq 2\) dimensions ⋮ Well-posedness and smoothing effect for generalized nonlinear Schrödinger equations ⋮ Ground states of Bose-Einstein condensates with higher order interaction ⋮ Wellposedness of some quasi-linear Schrödinger equations ⋮ Local well-posedness for the quasi-linear Hamiltonian Schrödinger equation on tori ⋮ Quasilinear Schrödinger equations. III: Large data and short time. ⋮ Global and local theory of skew mean curvature flows ⋮ Local well-posedness of skew mean curvature flow for small data in \(d\ge 4\) dimensions

Cites Work

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• Some remarks on the Cauchy problem
• The general quasilinear ultrahyperbolic Schrödinger equation
• Large data local solutions for the derivative NLS equation
• On some Schrödinger type equations
• Smoothing effects and local existence theory for the generalized nonlinear Schrödinger equations
• Variable coefficient Schrödinger flows for ultrahyperbolic operators
• Wave packet parametrices for evolutions governed by pdo's with rough symbols
• Introduction to nonlinear dispersive equations

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