The global-in-time existence of bounded weak solutions to the Maxwell–Stefan–Fourier equations in Fick–Onsager form is proved. The model consists of the mass balance equations for the partial mass densities and the energy balance equation for the total energy. The diffusion and heat fluxes depend linearly on the gradients of the thermo-chemical potentials and the gradient of the temperature and include the Soret and Dufour effects. The cross-diffusion system exhibits an entropy structure, which originates from the thermodynamic modeling. The lack of positive definiteness of the diffusion matrix is compensated by the fact that the total mass density is constant in time. The entropy estimate yields the a.e. positivity of the partial mass densities and temperature. Also diffusion matrices are considered that degenerate for vanishing partial mass densities.

证明了Fick-Onsager形式的Maxwell-Stefan-Fourier方程的有界弱解的全局时间性。该模型由部分质量密度的质量平衡方程式和总能量的能量平衡方程式组成。扩散和热通量线性依赖于热化学势的梯度和温度的梯度，并且包括索雷特效应和杜福尔效应。交叉扩散系统表现出一种熵结构，该结构源于热力学模型。总质量密度在时间上恒定这一事实弥补了扩散矩阵缺乏正定性的不足。熵估计得出部分质量密度和温度的正电性。