论文标题
在二维中，解决方案对klein-gordon-zakharov模型的渐近行为
Asymptotic Behavior of the Solution to the Klein-Gordon-Zakharov Model in Dimension Two
论文作者
论文摘要
考虑$ \ mathbb {r}^{1+2} $中的klein-gordon-Zakharov方程，我们有兴趣建立方程式的小全局解决方案，并在研究解决方案的渐近行为时。 Klein-Gordon-Zakharov方程可被视为具有二次非线性的耦合的半线性波和klein-Gordon系统，这些系统无法满足无效条件，并且波段和klein-gordon组件的事实并不能够充分快速衰减，因此很难进行分析。为了征服困难，我们将依靠倍增叶的方法和幽灵重量方法的较小差异。作为分析的另一个结果，我们还能够显示出一类准线性波和klein-gordon系统违反无效条件的小数据全局存在结果。
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.
