Global solutions for the Dirac-Proca equations with small initial data in 3+1 space time dimensions

DOI10.1016/S0022-247X(02)00662-5zbMath1020.35079OpenAlexW1987912809MaRDI QIDQ1874564

Yoshio Tsutsumi

Publication date: 25 May 2003

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0022-247x(02)00662-5

zbMATH Keywords

a priori estimatesCauchy problemunique global solutionDirac-Proca equations

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Second-order nonlinear hyperbolic equations (35L70) PDEs in connection with quantum mechanics (35Q40)

Related Items (15)

Global existence for systems of nonlinear wave and Klein-Gordon equations in two space dimensions under a kind of the weak null condition ⋮ Global existence for systems of nonlinear wave and Klein-Gordon equations with compactly supported initial data ⋮ Global evolution of the U(1) Higgs boson: nonlinear stability and uniform energy bounds ⋮ Stability of a coupled wave-Klein-Gordon system with quadratic nonlinearities ⋮ Boundedness of the conformal hyperboloidal energy for a wave-Klein-Gordon model ⋮ Asymptotic behavior of 2D wave-Klein-Gordon coupled system under null condition ⋮ Global behavior of small data solutions for the 2D Dirac–Klein-Gordon system ⋮ Stability of a coupled wave-Klein-Gordon system with non-compactly supported initial data ⋮ On the Cauchy problem for the semilinear Proca equations in the de Sitter spacetime ⋮ Global existence for coupled systems of nonlinear wave and Klein-Gordon equations in three space dimensions ⋮ Global solution to the wave and Klein-Gordon system under null condition in dimension two ⋮ Final state problem for the Dirac-Klein-Gordon equations in two space dimensions ⋮ Asymptotic behavior of the solution to the Klein-Gordon-Zakharov model in dimension two ⋮ Nonlinear scattering for a system of nonlinear Klein–Gordon equations ⋮ Global Solution to the Klein--Gordon--Zakharov Equations with Uniform Energy Bounds

Cites Work

• Global solution of the system of wave and Klein-Gordon equations
• The unit condition and global existence for a class of nonlinear Klein- Gordon equations
• Lectures on nonlinear hyperbolic differential equations
• Restriction theorems and semilinear Klein-Gordon equations in \((1+3)\)-dimensions
• Normal form and global solutions for the Klein-Gordon-Zakharov equations
• 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 solutions of nonlinear hyperbolic equations for small initial data
• Uniform decay estimates and the lorentz invariance of the classical wave equation
• Existence of global solutions of the Yang-Mills, Higgs and spinor field equations in $3+1$ dimensions
• Decay estimates for the Klein ndesh Gordon equation
• Asymptotic behavior of the solutions of maxwell—klein—gordon field equations in 4—dimensional minkowski space
• Small data blow-up for semilinear Klein-Gordon equations
• Weighted Sobolev spaces applied to nonlinear Klein-Gordon equation
• Asymptotic completeness, global existence and the infrared problem for the Maxwell-Dirac equations
• Global existence of small amplitude solutions for the Klein-Gordon-Zakharov equations
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