本项目研究流体力学方程的数学理论，重点研究不可压经典流体力学方程的正则性与边界层理论，研究多物理场作用的流体力学方程组的适定性与渐近极限问题，包括：研究多物理场作用下的复杂流体与经典流体之间的本质联系与多尺度结构稳定性问题、三维轴对称等特殊不可压流体力学方程和带分数阶的广义不可压流体模型的整体正则性与大初值解有限时刻爆破问题、多物理场耦合的复杂流体模型（核聚变电磁流体力学模型、外场作用下的粒子输运流体Fluid-Kinetic模型及其宏观两相流模型、粒子输运流体漂流扩散PNP-NS和PNP-E模型）各种波的稳定性理论与小参数极限多尺度结构稳定性问题，获得流体力学方程的正则性、边界层和结构稳定性方面的若干数学理论。. 本项目是偏微分方程研究领域的前沿课题，不仅具有重要的理论意义，而且在流体力学、受控核聚变、环境科学等应用科学有重要的指导意义。

The mathematical theory on fluid mechanics equations will be studied in this program. The special studies is to study regularity and boundary layer theory of classical incompressible fluid and to study well-posedness and asymptotic regimes of fluid mechanics equations coupled with multi-physical fields, which include: to study the relation between complex fluid coupled with multi-physical field and classical fluid and to obtain the multi-scaling structure stability on small parameters perturbation, to study global regularity and finite time blow-up on three-dimensional incompressible special fluid and their generalized models with the fractional order derivatives, and to study the stability of the waves and asymptotic regimes on complex fluid models coupled with multi-physical fields such as Electromagnetic fluid-dynamical equations in plasma and controlled nuclear fusion, Fluid-Kinetic models(VFP-NS or VFP-E) and drift-diffusion models (PNP-NS or PNP-E) in the transport theory of particles in fluid. Some mathematical theory on regularity, boundary layer theory and the stability of the multi-scaling structure of the systems will be established. . This program is of frontier in the field of nonlinear partial differential equations. There are of importance not only in theorical study and but also in applied sciences such as fluid mechanics, environmental science.