【摘 要】
：
The well-posedness of the Cauchy problem for the system (i(e)u+(e2x)u=uv+|u|2u,t,x∈R）(e)tu+(e)xH(e)xu=(e)x|u|2,u(0,x)=u0(x),v(0,x)=v0(x),is considered. It is pr
【机 构】
：
Graduate School, China Academy of Engineering Physics,P.O. Box 2101, Beijing, 100088, China“,”Instit
论文部分内容阅读
The well-posedness of the Cauchy problem for the system (i(e)u+(e2x)u=uv+|u|2u,t,x∈R）(e)tu+(e)xH(e)xu=(e)x|u|2,u(0,x)=u0(x),v(0,x)=v0(x),is considered. It is proved that there exists a unique local solution (u(x, t), v(x, t)) ∈C([O,T);Hs) × C([O,T);Hs-1/2) for any initial data (u0,v0) ∈ Hs(IR) × Hs-1/2(IR)(s ≥ 1/4)and the solution depends continuously on the initial data.
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