Global Solution for a Coupled Nonlinear Klein-Gordon System
-
摘要: 研究二维空间中一类耦合非线性Klein-Gordon方程组的整体解．首先，通过构造交叉强制变分问题且建立发展流的交叉不变流形，得到了该方程组解爆破和整体存在的一个最佳条件．然后利用尺度变换讨论证明了当初值为多小时,该方程组的整体解存在．
-
关键词:
- 耦合非线性Klein-Gordon方程组 /
- 整体解 /
- 爆破 /
- 交叉强制变分问题 /
- 最佳条件
Abstract: The global solution for a coupled nonlinear Klein-Gordon system in two space dimensions is studied.First,a sharp threshold of blowup and global existence for the system is obtained by constructing a type of cross-constrained variational problem and establishing so-called cross-invariant manifolds of the evolution flow.Then the result of how small the initial data are for which the solution of the system exists globally is proved by using the scaling argument. -
[1] Guo B L,Yuan G W. Global smooth solution for the Klein-Gordon-Zakharov equations[J].J Math Phys,1995,36(8):4119-4124. doi: 10.1063/1.530950 [2] Bachelot A.Problème de Cauchy globale pour des systèmes de Dirac-klein-Gordon[J].Ann Inst H Poincaré, Physique Théorique,1988,48(4):387-422. [3] Georgiev V.Global solution of the system of wave and Klein-Gordon equations[J].Math Z,1990,203(4):683-698. doi: 10.1007/BF02570764 [4] Georgiev V.Small amplitude solutions of the Maxwell-Dirac equations[J].Indiana Univ Math J,1991,40(3):845-883. doi: 10.1512/iumj.1991.40.40038 [5] Georgiev V. Decay estimates for the Klein-Gordon equations[J].Comm Part Diff Eqns,1992,17:1111-1139. [6] Zhang J.On the standing wave in coupled nonlinear Klein-Gordon equations[J].Math Meth Appl Sci,2003,26(1):11-25. doi: 10.1002/mma.340 [7] Segal I.Nonlinear semigroups[J].Annals of Mathematics,1963,78(2):339-364. doi: 10.2307/1970347 [8] Klainerman S. The null condition and global existence to nonlinear wave equations[J].Lect Appl Math,1986,23:293-326. [9] Klainerman S. Uniform decay estimates and the Lorentz invariance of the classical wave equations[J].Comm Pure Appl Math,1985,38(3):321-332. doi: 10.1002/cpa.3160380305 [10] Ozawa T, Tsutaya K,Tsutsumi Y.Normal formal form and global solutions for the Klein-Gordon-Zakharov equations[J].Annales de I'Institut Henri Poincaré,1995,12(4):459-503. [11] Shatah J. Normal forms and quadratic nonlinear Klein-Gordon equations[J].Comm Pure Appl Math,1985,38(5):685-696. doi: 10.1002/cpa.3160380516 [12] Sideris T.Decay estimates for the three-dimensional inhomogeneous Klein-Gordon equation and applications[J].Comm Part Diff Eqns,1989,14(10):1421-1455. doi: 10.1080/03605308908820660 -
计量
- 文章访问数: 2749
- HTML全文浏览量: 144
- PDF下载量: 794
- 被引次数: 0
下载:
渝公网安备50010802005915号