We study a system of equations of dynamics of a thermoviscoelastic continuous medium with an Oldroyd-type rheological relation, which generalizes a Navier–Stokes–Fourier system. In the planar case, we prove the unique existence of strong solutions. The proof is based on the construction of Galerkin approximations and their strong estimates, which provide the corresponding limit passage.

中文翻译：

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一种带记忆连续介质热粘弹性动力学模型的强解

我们研究了具有 Oldroyd 型流变关系的热粘弹性连续介质的动力学方程组，它概括了 Navier-Stokes-Fourier 系统。在平面情况下，我们证明了强解的唯一存在性。证明基于伽辽金近似及其强估计的构造，提供了相应的极限通道。