LOCAL WELL-POSEDNESS OF INTERACTION EQUATIONS FOR SHORT AND LONG DISPERSIVE WAVES

• 来源期刊: 偏微分方程(英文版)
• 学科: 数学
• 关键词: Short and long dispersive waves the Fourier restriction norm theSmoothing effects.
• 年，卷（期）: 2004,（2）
• 页码范围: 137-151
• 页数: 15页
• 分类号: O175.29
• 语种: 英文

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 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.