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arXiv · 2006.04443

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

Shijie Dong
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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.

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Shijie Dong. 2020-06-08. Asymptotic Behavior of the Solution to the Klein-Gordon-Zakharov Model in Dimension Two. https://doi.org/10.1007/s00220-021-04003-3

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