arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1107.3679math.AP
收藏

四维时空中非线性系统波动方程和Klein-Gordon方程小振幅解的整体存在性

Global existence of small amplitude solution to nonlinear system of wave and Klein-Gordon equations in four space-time dimensions

Yue MA

摘要:

在这篇文章中,将开发一个所谓的双曲面叶状方法,这是一个能量方法的基础上叶状的时空到双曲面超曲面。这种方法允许在同一框架内处理波动方程和Klein-Gordon方程,从而可以将其应用于波动方程和Klein-Gordon方程的耦合系统。作为应用,在一定条件下,我们将建立四维时空中具有二次非线性项的耦合波方程和Klei-Gordon方程小振幅解的整体存在性.与S. Katayama,本文中施加的条件允许包括一些重要的非线性项。所有这些都表明,这种方法可能是一种更自然的方式来看待波算子。

英文摘要:

In this article one will develop a so-called hyperboloidal foliation method, which is an energy method based on a foliation of space-time into hyperboloidal hypersurfaces. This method permits to treat the wave equations and the Klein-Gordon equations in the same framework so that one can apply it to the coupled systems of wave and Klein-Gordon equations. As an application, one will establish the global-in-time existence of small amplitude solution to the coupled wave and Klei-Gordon equations with quadratic nonlinearity in four space-time dimensions under certain conditions. Compared with those introduced by S. Katayama, the conditions imposed in this article permit to include some important nonlinear terms. All of these suggests that this method may be a more natural way of regarding the wave operator.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑