论文标题
3D中磁镀金弹性流体的适合度
Well-posedness for magnetoviscoelastic fluids in 3D
论文作者
论文摘要
我们表明，描述三维中磁性弹性流体的方程式可以作为准线性抛物线系统施放。使用最大$ l_p $ - 规范性的理论，我们确定了局部强解决方案的存在和独特性，并且我们表明每个解决方案在时空和时间上都是平滑的（实际上是分析）。此外，我们给出了一组均衡的完整表征，并表明从全球存在接近恒定平衡的溶液并收敛到（可能不同的）恒定平衡。最后，我们表明，最终在状态空间的拓扑中的每个解决方案都存在于全球，并融合到平衡集合中。
We show that the system of equations describing a magnetoviscoelastic fluid in three dimensions can be cast as a quasilinear parabolic system. Using the theory of maximal $L_p$-regularity, we establish existence and uniqueness of local strong solutions and we show that each solution is smooth (in fact analytic) in space and time. Moreover, we give a complete characterization of the set of equilibria and show that solutions that start out close to a constant equilibrium exist globally and converge to a (possibly different) constant equilibrium. Finally, we show that every solution that is eventually bounded in the topology of the state space exists globally and converges to the set of equilibria.
