Asymptotic Behavior of the Solution to the Klein-Gordon-Zakharov Model in Dimension Two

Abstract

Consider the Klein-Gordon-Zakharov equations in ${\mathbb{R}}^{1+2}$, and we are interested in establishing the small global solution to the equations and in investigating the pointwise asymptotic behavior of the solution. The Klein-Gordon-Zakharov equations can be regarded as a coupled semilinear wave and Klein-Gordon system with quadratic nonlinearities which do not satisfy the null conditions, and the fact that wave components and Klein-Gordon components do not decay sufficiently fast makes it harder to conduct the analysis. In order to conquer the difficulties, we will rely on the hyperboloidal foliation method and a minor variance of the ghost weight method. As a side result of the analysis, we are also able to show the small data global existence result for a class of quasilinear wave and Klein-Gordon system violating the null conditions.

24 pages, all comments are welcome

References in corpus (6)

• Stability of a coupled wave-Klein-Gordon system with quadratic nonlinearities
• Global solutions of nonlinear wave-Klein-Gordon system in two spatial dimensions: weak coupling case
• Global solutions of non-linear wave-Klein-Gordon system in two space dimension: semi-linear interactions
• Global solution to the wave and Klein-Gordon system under null condition in dimension two
• The Einstein-Klein-Gordon coupled system: global stability of the Minkowski solution
• The zero mass problem for Klein-Gordon equations

Cited by in corpus (6)

• Two dimensional wave--Klein-Gordon equations with semilinear nonlinearities
• Global solutions of nonlinear wave-Klein-Gordon system in two spatial dimensions: A prototype of strong coupling case
• Free Hyperboloidal Evolution of the Einstein-Maxwell-Klein-Gordon System
• 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 and Scattering of the Klein-Gordon-Zakharov System in Two Space Dimensions
• Global existence for 2-D wave maps equation in exterior domains