The existence of weak solutions to the Navier–Stokes–Fourier system describing the stationary states of a compressible, viscous, and heat conducting fluid in bounded $2\mathrm{D}$-domains is shown under fairly general and physically relevant constitutive relations. The equation of state of a real fluid is considered, where the admissible range of density is confined to a bounded interval (hard sphere model). The transport coefficients depend on the temperature in a general way including both gases and liquids behavior. The heart of the paper are new a priori bounds resulting from Trudinger–Moser inequality.

中文翻译：

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Navier–Stokes–Fourier系统在不可渗透边界的平面区域内的平稳解

Navier–Stokes–Fourier系统的弱解的存在，该系统描述了有界，可压缩，粘性和导热流体的稳态 $2\mathrm{d}$域是在相当普遍且与物理相关的本构关系下显示的。考虑真实流体的状态方程，其中允许的密度范围限于有界区间（硬球模型）。传输系数通常取决于温度，包括气体和液体的行为。本文的核心是由Trudinger-Moser不等式引起的新的先验边界。