Remark on local solvability of the Cauchy problem for semirelativistic equations

DOI10.1016/j.jmaa.2015.07.009zbMath1325.35200OpenAlexW900900049MaRDI QIDQ493801

Kazumasa Fujiwara

Publication date: 4 September 2015

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.2015.07.009

zbMATH Keywords

semirelativistic equationtest function methodnonexistence of local solutions

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items (4)

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 ⋮ 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

Cites Work

• Unnamed Item
• Small data blow-up of \(L^2\)-solution for the nonlinear Schrödinger equation without gauge invariance.
• On a system of semirelativistic equations in the energy space
• Nondispersive solutions to the \(L ^{2}\)-critical half-wave equation
• Some non-existence results for the semilinear Schrödinger equation without gauge invariance
• Some nonexistence results for a semirelativistic Schrödinger equation with nongauge power type nonlinearity
• Existence of ground states for a one-dimensional relativistic Schrödinger equation
• Existence and stability of standing waves for nonlinear fractional Schrödinger equations
• Biow-up of solutions of some nonlinear hyperbolic equations
• On the Semirelativistic Hartree‐Type Equation

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