多物理场耦合的可压流体动力学模型及其相关模型的适定性与渐近极限问题研究

Well-posedness and asymptotic limits of some nonlinear partial differential equations arising from multi-physical fields will be studied in this program. Special studies include: large time decay rate with respect to time, global stability of non-constant steady state, quasineutral limits and boundary layer problem on the isentropic or non-isentripic electromagnetic fluid-dynamical equations, and quasi-neutral limit of bipolar drift-diffusion equations for semiconductor with physical boundary conditions; large time decay rate with respect to time, global stability of non-constant steady state, singular fluid-dynamical limits of small parameters of Kinetic-Fluid models describing the interaction of particle and fluid arising from air pollution etc, and global well-posedness and small mach number limit of the related macroscopic fluid-dynamical models. The essential relations between the fluid-dynamical models with physical fields and classic fluid models, and mathematical theory of PN-junction for semiconductors will be established.. This program is of frontier in the field of nonlinear evolutionary equations. There are of importance not only in theorical study and but also in applied sciences such as controled fusion,aerospace,plasmas,semiconductor, air pollution(i.e.smog regimes)

本项目研究多物理场耦合的一些非线性偏微分方程组的适定性与渐近极限问题，重点研究等离子体物理中可压等熵和非等熵电磁流体动力学方程组非常数平衡解的稳定性与大时间衰减速率估计、拟中性极限与边界层问题，以及相关的半导体双极漂流扩散方程组在物理边界条件下的拟中性极限问题；空气污染中带外势场的粒子流体相互作用下的动理学流体耦合方程组的非常数平衡解的稳定性与大时间衰减估计、小参数宏观流体动力学奇异极限，以及相应的宏观流体动力学模型的整体适定性和小马赫数极限问题等。组建带物理场的流体和经典流体之间的本质联系以及半导体PN结内层的数学理论。. 本项目是国际非线性发展方程研究领域的前沿课题，不仅具有重要的理论意义，而且在受控核聚变、航空航天、等离子体物理和空气污染特别是雾霾机理等应用科学有重要的指导意义。

本项目研究了多物理场耦合的一些非线性偏微分方程组的适定性与渐近极限问题，重点研究了等离子体物理中可压等熵和非等熵电磁流体动力学方程组非常数平衡解的稳定性与大时间衰减速率估计、拟中性极限与边界层问题，以及相关的半导体双极漂流扩散方程组在物理边界条件下的拟中性极限问题；空气污染等应用科学中复杂动理学流体耦合方程组的非常数平衡解的稳定性与大时间衰减估计、小参数宏观流体动力学奇异极限，以及相应的宏观流体动力学模型的整体适定性和小马赫数极限问题等。组建了带物理场的流体和经典流体之间的本质联系以及复杂流体动力学模型的结构稳定性理论。在《Journal of Differential Equations》、《Journal of Dynamics and Differential Equations》、《Mathematical Models and Methods in Applied Sciences》、《Applied Mathematics Letters》、《Nonlinear Analysis-Theory Methods & Applications》、《Mathematical Methods in the Applied Sciences》等期刊上发表学术论文19篇，其中SCI收录论文16篇。已经圆满完成了项目预定的任务，实现了预定的目标。. 本项目是国际非线性发展方程研究领域的前沿课题，不仅具有重要的理论意义，而且在受控核聚变、航空航天、等离子体物理和空气污染特别是雾霾机理等应用科学有重要的指导意义。