Some nonexistence results for a semirelativistic Schrödinger equation with nongauge power type nonlinearity

DOI10.1090/proc/12938zbMath1342.35339OpenAlexW2318214197MaRDI QIDQ2802110

Takahisa Inui

Publication date: 25 April 2016

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/proc/12938

zbMATH Keywords

test functionnonexistence of global solutionsemirelativistic equations

Mathematics Subject Classification ID

A priori estimates in context of PDEs (35B45) NLS equations (nonlinear Schrödinger equations) (35Q55) Weak solutions to PDEs (35D30)

Related Items (11)

Wellposedness for semirelativistic Schrödinger equation with power-type nonlinearity ⋮ First and second critical exponents for an inhomogeneous Schrödinger equation with combined nonlinearities ⋮ Blowup results for the fractional Schrödinger equation without gauge invariance ⋮ Note on the lifespan estimate of solutions for non-gauge invariant semilinear massless semirelativistic equations with some scaling critical nonlinearity ⋮ Lifespan of strong solutions to the periodic nonlinear Schrödinger equation without gauge invariance ⋮ Fractional derivatives of composite functions and the Cauchy problem for the nonlinear half wave equation ⋮ Remark on local solvability of the Cauchy problem for semirelativistic equations ⋮ Lifespan estimates of 1D non-gauge invariant semilinear semirelativistic equations ⋮ On global well-posedness for nonlinear semirelativistic equations in some scaling subcritical and critical cases ⋮ A special form of solution to half-wave equations ⋮ Some nonexistence results for space-time fractional Schrödinger equations without gauge invariance

Cites Work

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• Nondispersive solutions to the \(L ^{2}\)-critical half-wave equation
• Some non-existence results for the semilinear Schrödinger equation without gauge invariance
• Blow up of solutions to semilinear wave equations with critical exponent in high dimensions
• A blow-up result for a nonlinear wave equation with damping: The critical case
• Existence of ground states for a one-dimensional relativistic Schrödinger equation
• A note on the lifespan of solutions to the semilinear damped wave equation
• Critical exponent for a nonlinear wave equation with damping

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