Large time behavior of the solutions to the equations of fluid motion.

在本研究中，我们考虑描述可压缩粘性流体运动的双曲型和抛物型非线性对称方程组。 对于这个系统，我们证明了在半空间中驻波的存在性和渐近稳定性。 我们证明了驻波存在的条件是由负特征的数量来表征的。 在Shizuta-Kawashima型稳定性条件下，利用能量方法证明了在适当的Sobolev空间中驻波的渐近稳定性。

In the present research, we consider the nonlinear symmetric systems of hyperbolic and parabolic type which describe the motion of compressible and viscous fluids. For this system, we show the existence and asymptotic stability of stationary waves in a half space. We show that the condition for the existence of stationary waves is characterized by the number of negative characteristics. We also prove the asymptotic stability of the stationary waves in a suitable Sobolev space by using the energy method under the stability condition of Shizuta-Kawashima type.