We study the zero viscosity and thermal diffusivity limit of an initial boundary problem for the linearized Navier–Stokes–Fourier equations of a compressible viscous and heat conducting fluid in the half plane. We consider the case that the viscosity and thermal diffusivity converge to zero at thesame order. The approximate solution of the linearized Navier–Stokes–Fourier equations with inner and boundary expansion terms is analyzed formally first by multiscale analysis. Then the pointwise estimates of the error terms of the approximate solution are obtained by energy methods. Thus establish the uniform stability for the linearized Navier–Stokes–Fourier equations in the zero viscosity and heat conductivity limit. This work is based on (Comm. Pure Appl. Math. 52 (1999), 479–541) and generalize their results from isentropic case to the general compressible fluid with thermal diffusive effect. Besides the viscous layer as in (Comm. Pure Appl. Math. 52 (1999), 479–541), the thermal layer appears and couples with the viscous layer linearly.

中文翻译：

---

线性可压缩的Navier–Stokes–Fourier方程在半平面中的零粘度和热扩散极限

我们研究了半平面中可压缩粘性和导热流体的线性Navier–Stokes–Fourier方程的初始边界问题的零粘度和热扩散极限。我们考虑了粘度和热扩散率以相同顺序收敛到零的情况。首先通过多尺度分析来正式分析带有内部和边界扩展项的线性化Navier–Stokes–Fourier方程的近似解。然后通过能量方法获得近似解的误差项的逐点估计。因此，在零粘度和热导率极限下，为线性化的Navier–Stokes–Fourier方程建立了统一的稳定性。这项工作基于（Comm。Pure Appl。Math。52（1999），479-541），并将其结果从等熵情况推广到具有热扩散作用的一般可压缩流体。除了（Comm。Pure Appl。Math。52（1999），479-541）中的粘性层之外，还会出现热层并与粘性层线性耦合。