数学物理学报(英文版) ›› 1998, Vol. 18 ›› Issue (1): 25-34.
赵会江1, 柳再华2, 陈世平3
Zhao Huijiang1, Liu Zaihua2, Chen Shiping3
摘要: In this paper, it is considered that the global existence, uniqueness and regularity results for the Cauchy problem of the well-known Kuramoto-Stvashinsky equation
ut+1/2▽(|u|2)+△u+△2u=0,t>0,x∈RN, u(0,x)=u0(x),x∈RN.
only under the condition u0(x) ∈L2(RN, Rn). Where u(t, x)=(u1 (t, x),…,un (t, x))T is the unknown vector-valued function. Results show that for N < 6,u0 (x) ∈L2 (RN, Rn), the above Cauchy problem admits a unique global solution u(t, z) which belongs to C∞,∞ (RN×(0, ∞)).