半空间一维可压缩Navier-Stokes方程解的渐进性

讨论了半空间中满足无渗透边界条件的一维黏性可压缩热传导流体的流动，给出了在小扰动和非等温条件下稀疏波的渐进稳定性。当速度在边界上为零时，证明了一维可压缩Navier-Stokes方程的解在半空间中随时间的增大而趋向于本文所定义的3-稀疏波。所用的证明方法为能量方法。

Asymptotic behavior of solutions to the full compressible Navier-Stokes equations in the half space

One-dimensional compressible viscous and heat conductive fluid flow has been investigated in the half space. The asymptotic stability of the rarefaction wave has been established for the impermeable wall problem under small perturbation conditions and non-isothermal conditions. If the velocity is zero at the boundary, the solution of the Navier-Stokes equations is shown to tend toward a 3-rarefaction wave which has been defined. The proof is given by prior estimate and elementary energy method.