We prove that there exists a large-data and global-in-time weak solution to a system of partial differential equations describing the unsteady flow of an incompressible heat-conducting rate-type viscoelastic stress-diffusive fluid filling up a mechanically and thermally isolated container of any dimension. To overcome the principal difficulties connected with ill-posedness of the diffusive Oldroyd-B model in three dimensions, we assume that the fluid admits a strengthened dissipation mechanism, at least for excessive elastic deformations. All the relevant material coefficients are allowed to depend continuously on the temperature, whose evolution is captured by a thermodynamically consistent equation. In fact, the studied model is derived from scratch using only the balance equations for linear momentum and energy, the formulation of the second law of thermodynamics and the constitutive equation for the internal energy. The latter is assumed to be a linear function of temperature, which simplifies the model. The concept of our weak solution incorporates both the temperature and entropy inequalities, and also the local balance of total energy provided that the pressure function exists.

我们证明，描述填充机械和热隔离容器的不可压缩导热率型粘弹性应力扩散流体的非定常流动的偏微分方程组存在大数据和全局时间弱解。任何维度的。为了克服与三维扩散 Oldroyd-B 模型不适定相关的主要困难，我们假设流体允许强化耗散机制，至少对于过度弹性变形而言。所有相关的材料系数都可以连续依赖于温度，其演变由热力学一致方程捕获。事实上，所研究的模型是仅使用线性动量和能量的平衡方程、热力学第二定律的公式以及内能的本构方程从头开始推导的。假设后者是温度的线性函数，这简化了模型。我们的弱解的概念包含了温度和熵不等式，以及总能量的局部平衡（只要存在压力函数）。