两分量Novikov系统初值问题解的局部Gevrey正则性与解析性

Local Gevrey regularity and analyticity of the solutions to the initial value problem associated with the two-component Novikov system

利用一个推广的Ovsyannikov定理,讨论了两分量Novikov系统Cauchy问题解在Sobolev-Gevrey空间G 1 r,s(R)×G 1 r,s-1(R)中的正则性与解析性,其中s>3/2,r≥1,并研究了该问题解映射z0→z(t)的连续性。此结论可以直接应用到Novikov方程。

Considered herein is the initial value problem for the two-component Novikov system.At first,the Gevrey regularity and analyticity of the solutions to this problem in Sobolev-Gevrey spaces G 1 r,s(R)×G 1 r,s-1(R)with s>3/2,r≥1 are investigated by making use of the generalized Ovsyannikov theorem.Next,the continuity of the solution map z0→z(t)is discussed.The results can be directly applied to Novikov equation.