可压缩Navier-Stokes-Maxwell 方程组解的适定性研究

The research on hydrodynamic equations such as Naver-Stokes equations, the most typical example, has attracted more and more attention from many mathematicians and physicists. The project is mainly concerned with the motion of the electrically conducting fluid under the influence of the electromagnetic field, which can be described by the compressible Navier-Stokes equations coupled with Maxwell equations through the Lorentz force, the so-called "Navier-Stokes-Maxwell equations". The investigation of the model could be applied in many fields such as gasdynamic, astrophysics , plasma physics and so on. Meanwhile, the study of this system will provide important reference to explain some physical phenomena. I will investigate theoretically the global existence of solutions to three-dimensional compressible isentropic Navier-Stokes-Maxwell equations, as well as one-dimensional non-isentropic model. It is expected to obtain the global classical solutions for Cauchy problems with large initial data. Compared with the classical Navier-Stokes equations, the difficulty mainly comes from the coupling of electromagnetic field and fluid flow.

以Navier-Stokes方程组为典型代表的方程的研究一直备受许多数学家和物理学家的关注。本项目主要研究带电流体在电磁场中的运动，其运动规律可由可压缩Navier-Stokes方程组通过洛伦兹力耦合Maxwell方程组来描述(Navier-Stokes-Maxwell方程组)。该模型的研究在气体动力学、天体物理、等离子物理等领域中有广泛的应用。随着该模型某些问题的解决将会对解释某些物理现象提供重要参考。本项目拟围绕三维等熵可压缩Navier-Stokes-Maxwell方程组以及一维非等熵Navier-Stokes-Maxwell方程组解的整体存在性展开系统研究，期望得到上述Cauchy问题大初值经典解的整体存在性。与经典的Navier-Stokes方程组相比，需要克服由电磁场与流场的耦合所导致的困难。

项目背景：本项目主要研究Navier-Stokes-Maxwell方程组，它描述了带电流体(主要是等离子体)在电磁场中的运动，其数学结构是经典的 Navier-Stokes 方程组通过洛伦兹力耦合 Maxwell 方程组。该模型的研究在气体动力学、天体物理、等离子物理等领域中有广泛的应用。主要研究内容：本项目拟围绕三维等熵可压缩Navier-Stokes-Maxwell方程组以及一维非等熵Navier-Stokes-Maxwell方程组解的整体存在性展开系统研究，期望得到上述Cauchy问题大初值经典解的整体存在性。与经典的Navier-Stokes方程组相比，需要克服由电磁场与流场的耦合所导致的困难。.重要结果：对于NSM 方程组的研究仍在继续，相应的研究成果还未发表。.科学意义：该模型的研究在气体动力学、天体物理、等离子物理等领域中有广泛的应用。因此，对 NSM 方程组的研究必将会对解释某些物理现象、力学规律提供重要的参考。这些问题的数学理论研究非常困难而且富有挑战性，尤其是其整体适定性的研究。