偏微分方程组的渐近极限问题是偏微分方程理论研究的重要分支之一。流体力学方程组的低马赫数极限问题和半导体模型的拟中性极限问题是两类来源于物理的偏微分方程组的渐近极限问题，本质上是奇异极限问题，是当前偏微分方程研究的前沿问题，具有重要的理论意义和坚实的应用背景，同时也富有挑战性。. 本项目重点研究用于描述理想的多方气体的非等熵可压缩Navier-Stokes方程组的一般初始值和温度大变差情形下的低马赫数极限问题和有界区域中的粘弹性流体方程组的低马赫数极限问题（包括三维有界区域中具有滑动边界条件的Oldroyd-B模型的整体强解的低马赫数极限问题和具有滑动边界条件的带有扩散应力的二维Oldroyd-B模型的低马赫数极限问题）；同时开展对三维空间中掺杂分布光滑变号的情况下的半导体漂流扩散模型的拟中性极限的研究。

Asymptotic limit in partial differential equations is one of the important branches of the research on partial differential equations. The low Mach number limit in fluid dynamics and the quasi-neutral limit of semiconductor models are two kinds of asymptotic limit in partial differential equations originating from physics. They are essentially singular limits which are frontier problems in the research of partial differential equations. They have important theoretical significance and solid application background, and are also challenging. . The present project mainly considers the low Mach number limit of non-isentropic compressible Navier-Stokes equations for perfect gas with general initial data and large temperature variation and the one of viscoelastic fluid equations in the bounded domain (including the low Mach number limit of the global strong solutions to the three-dimensional Oldroyd-B model with slip boundary conditions and two-dimensional Oldroyd-B model with diffusive stress with slip boundary conditions . Meanwhile, the quasi-neutral limit of three-dimensional drift-diffusion models for semiconductor with smooth sign-changing doping profile will also be considered.