Well-posedness of the Cauchy problem for Ostrovsky, Stepanyams and Tsimring equation with low regularity data

作者：Zhao, Xiangqing^*; Cui, Shangbin

来源：Journal of Mathematical Analysis and Applications, 2008, 344(2): 778-787.

DOI：10.1016/j.jmaa.2008.03.032

• OST equation
• initial value problem
• local well-posedness
• global well-posedness

this paper we prove that the initial value problem of the OST equation u(t) u(xxx) eta(Hu(x) Hu(xxx)) uu(x) = 0 (x is an element of R, t >= 0), where eta > 0 and H denotes the usual Hilbert transformation, is locally well-posed in the Sobolev space H-s(R) when s > -3/4, and globally well-posed in H-s(R) when s >= 0.

• 出版日期2008-8-15
• 单位中山大学; 浙江海洋大学