磁粘弹性流体演化模型的类Struwe解
Struwe-like solutions for an evolutionary model of magnetoviscoelastic fluids
摘要：
在这项工作中，我们调查的存在性和唯一性的Struwe类解的偏微分方程组系统的动力学建模的磁粘弹性流体。所考虑的系统耦合的Navier-Stokes型方程与耗散方程的变形张量和Landau-Lifshitz-Gilbert型方程的磁化场。主要目的是建立一个适定性理论在一个二维周期域的标准假设下的临界正则性（可能大）的初始数据。我们证明了所考虑的弱解是处处光滑的，除了一个离散集的时间值。证明的唯一性是基于适当的能量估计的功能框架内的解决方案，这是不太经常比一个Struwe能量水平。这些估计依赖于几种技术的调和分析和paradifferential微积分。
英文摘要：
In this work we investigate the existence and uniqueness of Struwe-like solutions for a system of partial differential equations modeling the dynamics of magnetoviscoelastic fluids. The considered system couples a Navier-Stokes type equation with a dissipative equation for the deformation tensor and a Landau-Lifshitz-Gilbert type equation for the magnetization field. The main purpose is to establish a well-posedness theory in a two-dimensional periodic domain under standard assumption of critical regularity for the (possibly large) initial data. We prove that the considered weak solutions are everywhere smooth, except for a discrete set of time values. The proof of the uniqueness is based on suitable energy estimates for the solutions within a functional framework which is less regular than the one of the Struwe energy level. These estimates rely on several techniques of harmonic analysis and paradifferential calculus.
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