利用Sobolev空间相应的知识以及一些不等式,研究有界区域内广义Ostrovsky方程解的存在性与唯一性问题,得到几个先验估计.通过应用Galerkin方法,证明在给定的初始条件下非线性强度为2的广义Ostrovsky方程存在唯一的整体解.
Cauchy problem for the generalized Ostrovsky equation in bounded domain is studied. By applying some knowledges of Sobolev space and some inequalities, some a prior estimations are obtained. By using Galerkin method it is proved that there exists a unique global solution for the generalized Ostrovsky equation in bounded domain.