On Nonlinear Schrödinger Equations with Almost Periodic Initial Data

DOI10.1137/140973384zbMath1334.35322arXiv1405.7330OpenAlexW2161879856MaRDI QIDQ5253458

Tadahiro Oh

Publication date: 26 May 2015

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1405.7330

zbMATH Keywords

almost periodic functionsnonlinear Schrödinger equationlocal well-posednessfinite time blowup solution

Mathematics Subject Classification ID

Almost and pseudo-almost periodic solutions to PDEs (35B15) Classical almost periodic functions, mean periodic functions (42A75) NLS equations (nonlinear Schrödinger equations) (35Q55) Harmonic analysis and almost periodicity in probabilistic number theory (11K70) Blow-up in context of PDEs (35B44)

Related Items (8)

On nonlinear Schrödinger equations with random initial data ⋮ On the probabilistic well-posedness of the nonlinear Schrödinger equations with non-algebraic nonlinearities ⋮ The nonlinear Schrödinger equation on Z and R with bounded initial data: examples and conjectures ⋮ The quasi-periodic Cauchy problem for the generalized Benjamin-Bona-Mahony equation on the real line ⋮ Some non-existence results for the semilinear Schrödinger equation without gauge invariance ⋮ Uniqueness of solutions of the KdV-hierarchy via Dubrovin-type flows ⋮ Global well-posedness for the cubic nonlinear Schrödinger equation with initial data lying in L p-based Sobolev spaces ⋮ Global existence for the defocusing nonlinear Schrödinger equations with limit periodic initial data

Cites Work

• 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.
• On solutions of nonlinear Schrödinger equations with Cantor-type spectrum
• Blow-up results for nonlinear parabolic equations on manifolds
• Global existence for the defocusing nonlinear Schrödinger equations with limit periodic initial data
• On the existence and uniqueness of global solutions for the KdV equation with quasi-periodic initial data
• Local Well-Posedness of the KdV Equation with Quasi-Periodic Initial Data
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