KdVKS方程的局部适定性（英文）

ON THE LOCAL WELL-POSEDNESS FOR THE KDVKS EQUATION

本文研究了KdVKS方程u_t+δ?_x^3u+μ(?_x^4u+?_x^2u)+α(?_xu)~2=0的Cauchy问题.利用Tao的[k;Z]乘子范数估计的方法,在Sobolev空间Hs(R),s>-1中证明了初值问题的局部适定性,结论改进了现有的Biagioni等的结果.

In this paper, we consider the Cauchy problem for the Kd VKS equation ut＋δδx^3 u ＋ μ（δx^4 u ＋ δx^2 u） ＋ α（δxu）^2= 0. By means of the [k; Z] multiplier norm method of Tao, we prove the associated initial value problem is locally well-posed in Sobolev spaces Hs（R） for s -1,which improves the conclusions drawn by Biagioni et al.