Finite time blowup of solutions to the nonlinear Schrödinger equation without gauge invariance

DOI10.1063/1.4960725zbMath1348.35231OpenAlexW2510153142MaRDI QIDQ2820892

Kazumasa Fujiwara, Tohru Ozawa

Publication date: 12 September 2016

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.4960725

zbMATH Keywords

nonlinear Schrödinger equationfinite time blowup

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Initial value problems for nonlinear higher-order PDEs (35G25) Blow-up in context of PDEs (35B44)

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Sharp upper bound for lifespan of solutions to some critical semilinear parabolic, dispersive and hyperbolic equations via a test function method ⋮ \(L^p\)-\(L^q\) estimates for the damped wave equation and the critical exponent for the nonlinear problem with slowly decaying data ⋮ A test function method for evolution equations with fractional powers of the Laplace operator ⋮ On the lifespan of strong solutions to the periodic derivative nonlinear Schrödinger equation ⋮ Blow-up phenomena of semilinear wave equations and their weakly coupled systems ⋮ Global well-posedness for the semilinear wave equation with time dependent damping in the overdamping case ⋮ Remark on upper bound for lifespan of solutions to semilinear evolution equations in a two-dimensional exterior domain ⋮ Estimates of Lifespan and Blow-up Rates for the Wave Equation with a Time-dependent Damping and a Power-type Nonlinearity ⋮ Lifespan of solutions for a weakly coupled system of semilinear heat equations

Cites Work

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• A blowup result for the periodic NLS without gauge invariance
• Small data blow-up of \(L^2\)-solution for the nonlinear Schrödinger equation without gauge invariance.
• Small data blow-up of \(L^2\) or \(H^1\)-solution for the semilinear Schrödinger equation without gauge invariance
• Lifespan of strong solutions to the periodic nonlinear Schrödinger equation without gauge invariance
• Blow-up results for nonlinear parabolic equations on manifolds
• Some non-existence results for the semilinear Schrödinger equation without gauge invariance
• A blow-up result for a nonlinear wave equation with damping: The critical case
• Life-span of smooth solutions to the complex Ginzburg–Landau type equation on a torus

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