We introduce a system of equations that models a non-isothermal magnetoviscoelastic fluid. We show that the model is thermodynamically consistent, and that the critical points of the entropy functional with prescribed energy correspond exactly with the equilibria of the system. The system is investigated in the framework of quasilinear parabolic systems and shown to be locally well-posed in an \(L_p\)-setting. Furthermore, we prove that constant equilibria are normally stable. In particular, we show that solutions that start close to a constant equilibrium exist globally and converge exponentially fast to a (possibly different) constant equilibrium. Finally, we establish that the negative entropy serves as a strict Lyapunov functional and we then show that every solution that is eventually bounded in the topology of the natural state space exists globally and converges to the set of equilibria.

我们引入了一个模拟非等温磁粘弹性流体的方程组。我们证明该模型在热力学上是一致的，并且具有指定能量的熵泛函的临界点与系统的平衡完全一致。该系统在拟线性抛物线系统的框架中进行了研究，并显示在\(L_p\)设置中局部适定。此外，我们证明恒定平衡通常是稳定的。特别是，我们表明，从接近恒定平衡开始的解在全局范围内存在，并且以指数方式快速收敛到（可能不同的）恒定平衡。最后，我们建立负熵作为严格的李亚普诺夫函数，然后证明最终在自然状态空间拓扑中受限的每个解全局存在并收敛到均衡集。