KP型方程和Ostrovsky型方程是描述水波传播的两类重要的色散波方程。本项目主要用来研究KP型方程和Ostrovsky型方程的的低正则性问题。具体说来，内容主要涉及到两个方面。(1) 使用算子半群理论、修正Sobolev空间、各向异性Sobolev空间、修正Besov空间、原子空间、修正傅里叶限制范数方法、Strichartz估计、Littlewood-Paley分解以及一些基本的代数恒等式，研究KP型方程在周期情形与非周期情形时的局部适定性、整体适定性和散射性。(2)使用修正傅里叶限制范数方法、Strichartz估计以及一些基本的代数恒等式，研究Ostrovsky型方程在Sobolev空间中的局部适定性、不适定性、整体适定性以及散射性。

KP-type equations and Ostrovsky-type equations are two kinds of important dispersive equations， which describe the propagation of water waves. This project mainly studies the low regularity of the KP-type equations and the Ostrovsky-type equations. More concretely, this project mainly includes two parts. (1)By using the theory of semigroup of operators、modified Sobolev spaces、anisotropic Sobolev spaces、modified Besov spaces、atomic spaces、modified Fourier restriction norm method、Strichartz estimates、Littlewood-Paley decomposition and some elementary algebraic identities，this project studies the local well-posedness、global well-posedness and scattering of KP-type equations in the periodic case and in the nonperiodic case. (2)By using the modified Fourier restriction norm method、 Strichartz estimates and some elementary algebraic identities, this project studies the local well-posedness、 global well-posedness、ill-posedness and scattering of Ostrovsky-type equations in the Sobolev spaces.