本项目拟通过发展现代分析的方法，研究流体力学与量子力学中出现的某些偏微分方程的数学理论，主要涉及：通过发展物理空间与频率空间的局部化技术研究Maxwell-Navier-Stokes 方程等流体动力学方程；通过发展含位势的Laplace算子对应的调和分析理论、结合Kenig-Merle的集中紧/刚性方法研究含位势的非线性色散方程的散射理论；通过研究离散限制性估计、波包分解及相应的微局部分析，结合堆垒数论中的三角级数的平均求和法，研究光滑紧流形上的非线性色散方程等。

The project intends to study the mathematical theory of some partial differential equations which appear in fluid mechanics and quantum mechanics by developing the modern analysis methods, mainly related to: the research on the mathematical theory of the fluid dynamics equations such as Maxwell-Navier-Stokes equations; the research on scattering theory of nonlinear dispersive equation with potential by developing the harmonic analysis theory associated with Laplacian with potential , combining the argument of concentration compactness/rigidity developed by Kenig-Merle; the research of nonlinear dispersive equations on smooth compact Reimann manifold by studying discrete restriction estimates, wave packet decomposition and the corresponding micro-local analysis, combined with summation of trigonometric series average appearing in additive number theory.