Ostrovsky方程的Cauchy问题

Cauchy Problem of Ostrovsky Equation

研究Ostrovsky方程的Cauchy问题{u_2+αu_(xxx)+u_x+((u^p)_x)_x=yu, u(x,0)=φ(x),其中,x∈R,t≥0,α、β、γ是常数,p≥2是正整数.证明了该问题的解在空间χ_s中的局部存在性和解在空间χ_2中的整体存在性.

This paper deals with the following Cauchy problem for the Ostrovsky equation{u2＋αu（xxx）＋ux＋（（u^p）x）x=yu, u（x,0）=φ（x）,（where x ∈ R,t≥0,α,β,γ are constants,p≥2 is a positive integer,and local and global-in-time solvability is investigated.We prove the local existence of solution in χs and global existence of solution in χ2.