A blowup result for the periodic NLS without gauge invariance

DOI10.1016/j.crma.2012.04.009zbMath1239.35149OpenAlexW1989591635MaRDI QIDQ424751

Tadahiro Oh

Publication date: 4 June 2012

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://www.pure.ed.ac.uk/ws/files/19920606/A_blowup_result_for_the_periodic_NLS_without_gauge_invariance.pdf

Mathematics Subject Classification ID

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

Related Items (12)

Blowup and ill-posedness results for a Dirac equation without gauge invariance ⋮ Small data blow-up for a system of nonlinear Schrödinger equations ⋮ Lifespan of strong solutions to the periodic nonlinear Schrödinger equation without gauge invariance ⋮ On the probabilistic well-posedness of the nonlinear Schrödinger equations with non-algebraic nonlinearities ⋮ Quasiperiodicity and blowup in integrable subsystems of nonconservative nonlinear Schrödinger equations ⋮ On global existence of L2 solutions for 1D periodic NLS with quadratic nonlinearity ⋮ Some non-existence results for the semilinear Schrödinger equation without gauge invariance ⋮ Small data blow-up of \(L^2\) or \(H^1\)-solution for the semilinear Schrödinger equation without gauge invariance ⋮ Finite time blowup of solutions to the nonlinear Schrödinger equation without gauge invariance ⋮ Global dynamics in nonconservative nonlinear Schrödinger equations ⋮ On Nonlinear Schrödinger Equations with Almost Periodic Initial Data ⋮ Nonlinear smoothing for the periodic generalized nonlinear Schrödinger equation

Cites Work

• Global well-posedness of the energy-critical nonlinear Schrödinger equation with small initial data in \(H^1(\mathbb T^3)\)
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I: Schrödinger equations
• Exponential sums and nonlinear Schrödinger equations
• Blow-up results for nonlinear parabolic equations on manifolds
• A blow-up result for a nonlinear wave equation with damping: The critical case
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