本项目拟运用调和分析, 微分算子半群理论以及泛函分析理论去研究描述水波运动的Ostrovsky方程和Kawahara型方程的Cauchy问题。内容主要涉及两个方面：(1)综合运用偏微分方程理论，结合算子半群理论，Fourier限制范数方法及其修正方法，修正的Bourgain空间，二进制双线性估计和不动点定理来研究Ostrovsky方程和Kawahara型方程的Cauchy问题在Sobolev或修正Sobolev空间中的局部适定性。（2)在局部适定性的基础上，选择合适的函数空间，利用I-方法或者修正的I-方法建立整体适定性。

In this project we will apply the theory of harmnoic analysis, semigroups of differential operators and functional analysis to study the Cauchy problems for Ostrovsky equation and Kawahara-type equation which describe the motion of water waves. The main content includes two parts: (1)Combining the theory of the partial differential equations with semigroup of operators, applying the Fourier restriction norm method and its modification, modified Bourgain spaces, dyadic bilinear estimates and fixed point theorem, we will study the local well-posedness of the Cauchy problems for Ostrovsky equation and Kawahara-type equations in Sobolev spaces or modified Sobolev spaces. (2)Based on the local well-posedness, by carefully choosing the suitable function spaces and applying the I-method or modified I-method, we will establish the global well-posedness.. . .