Sharp condition of global existence for second-order derivative nonlinear Schrödinger equations in two space dimensions

DOI10.1016/j.jmaa.2006.03.055zbMath1111.35086OpenAlexW1966105112MaRDI QIDQ865317

Jian Zhang, Ji Shu

Publication date: 14 February 2007

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2006.03.055

zbMATH Keywords

blow-upglobal existencenonlinear Schrödinger equations

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Variational methods applied to PDEs (35A15) NLS equations (nonlinear Schrödinger equations) (35Q55)

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Cites Work

• Nonlinear Schrödinger equations and sharp interpolation estimates
• Saddle points and instability of nonlinear hyperbolic equations
• On the existence of soliton solutions to quasilinear Schrödinger equations
• Soliton solutions for quasilinear Schrödinger equations. II.
• Evolution theorem for a class of perturbed envelope soliton solutions
• A Remark on the Blowing-Up of Solutions to the Cauchy Problem for Nonlinear Schrodinger Equations
• On the blowing up of solutions to the Cauchy problem for nonlinear Schrödinger equations
• Instability and Nonexistence of Global Solutions to Nonlinear Wave Equations of the Form Pu tt = -Au + ℱ(u)
• On the local well posedness of quasilinear Schrödinger equations in arbitrary space dimension
• An inverse function theorem in Sobolev spaces and applications to quasi-linear Schrödinger equations
• Sharp conditions of global existence for nonlinear Schrödinger and Klein-Gordon equations.
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