Notes on global existence for the nonlinear Schrödinger equation involves derivative

DOI10.1007/s10114-014-3534-4zbMath1304.35661OpenAlexW2104319585MaRDI QIDQ477849

Shi Yang Zheng

Publication date: 10 December 2014

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-014-3534-4

zbMATH Keywords

Schrödinger equationsmall dataglobal well-posednessquadraticscatter

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Nonlinear evolution equations (47J35) Blow-up in context of PDEs (35B44)

Cites Work

• Unnamed Item
• Global solutions for 2D quadratic Schrödinger equations
• Small data blow-up of \(L^2\)-solution for the nonlinear Schrödinger equation without gauge invariance.
• The Cauchy problem for the two dimensional Euler-Poisson system
• Global well-posedness for Schrödinger equation with derivative in \(H^{\frac {1}{2}} (\mathbb R)\)
• Modified wave operators for the derivative nonlinear Schrödinger equation
• Global well-posedness for the nonlinear Schrödinger equation with derivative in energy space
• Sharp linear and bilinear restriction estimates for paraboloids in the cylindrically symmetric case
• Global Solutions for 3D Quadratic Schrodinger Equations
• Resonance and long time existence for the quadratic semilinear schrödinger equation
• Strichartz estimates in spherical coordinates
• Maximal functions associated to filtrations

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