Asymptotic analysis of systems of nonlinear partial differential equations describing motions of viscous fluids

研究了描述粘性流体运动的可压缩Navier-Stokes方程解的渐近性质。我们详细分析了静止解和平行流等稳态解的稳定性。证明了这些平稳解在一定意义上足够小时是渐近稳定的。此外，还证明了扰动在大时间内表现为对流热方程的解。

We studied the asymptotic behavior of solutions of the compressible Navier-Stokes equation which describes motion of viscous fluids. We analyzed the stability properties of stationary solutions such as the motionless state and parallel flows in detail. It was proved that these stationary solutions are asymptotically stable if they are small enough in some sense. Furthermore, it was shown that the disturbances behave like solutions of convective heat equations in large time.