Asymptotic analysis of partial differential equations arising from fluid mechanics

对于流体力学中的偏微分方程组，我研究了可压缩粘性流体中满足Burgers涡的显式解，由于没有关于可压缩粘性流体中Burgers涡的数学结果，所以我在注意正压性的存在或不存在的情况下找到了显式解。在此基础上，对可压缩粘性非正压流体的Navier-Stokes方程进行了数学分析。

As for partial differential equations arising from fluid mechanics, I studied explicit solutions satisfying the Burgers vortex in a compressible viscous fluid.Since there was no mathematical result concerning the Burgers vortex in a compressible viscous fluid, I found the explicit solutions while paying attention to the existence or nonexistence of barotropicity. The achievement is to clarify that the nonbarotropic case is natural under the study of the Burgers vortex in a compressible viscous fluid.Based on this achievement, I am trying to study mathematical analysis of the Navier -Stokes equations for compressible viscous nonbarotropic fluids.