Restriction theorems and semilinear Klein-Gordon equations in \((1+3)\)-dimensions

DOI10.1215/S0012-7094-96-08510-5zbMath0865.35077OpenAlexW2045523850MaRDI QIDQ1816477

Christopher D. Sogge, Hans Lindblad

Publication date: 19 December 1996

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-96-08510-5

zbMATH Keywords

semiglobal existence result

Mathematics Subject Classification ID

Second-order nonlinear hyperbolic equations (35L70) Initial value problems for second-order hyperbolic equations (35L15)

Related Items (8)

Almost global existence for solution of semilinear klein-gordon equations with small weakly decaying cauchy data ⋮ Global solutions for the Dirac-Proca equations with small initial data in 3+1 space time dimensions ⋮ Existence of global decaying solutions to the exterior problem for the Klein-Gordon equation with a nonlinear localized dissipation and a derivative nonlinearity ⋮ Stability of a coupled wave-Klein-Gordon system with quadratic nonlinearities ⋮ Integral type Cauchy problem for abstract wave equations and applications ⋮ Boundedness of the conformal hyperboloidal energy for a wave-Klein-Gordon model ⋮ \(H^{s}\)-global well-posedness for semilinear wave equations ⋮ Existence globale et comportement asymptotique pour l'équation de Klein–Gordon quasi linéaire à données petites en dimension 1

Cites Work

• Transference principles for radial multipliers
• The unit condition and global existence for a class of nonlinear Klein- Gordon equations
• Space-time decay for solutions of wave equations
• Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations
• Blow-up of solutions of nonlinear wave equations in three space dimensions
• Inequalities for strongly singular convolution operators
• Blow-up for solutions of □u=|u|^pwith small initial data.
• Global existence of small amplitude solutions to nonlinear klein-gordon equations in four space-time dimensions
• Normal forms and quadratic nonlinear Klein-Gordon equations
• Global solution to the two–dimensional klein–gordon equation
• Remark on the asymptotic behavior of the klein gordon equation in ℝⁿ⁺¹
• Long-time existence for small amplitude semilinear wave equations
• A restriction theorem for the Fourier transform
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