关键词: 适定弱解, 部分正则性, 磁-粘弹性流, Hausdorff 维数

Abstract: In this paper, inspired by the celebrated work of Caffarelli et al. [2]on partial regularity for the classic incompressible Navier-Stokes system and by Du et al. [4] on suitable weak solutions for the co-rotational Beris-Edwards system, we establish the global existence of suitable weak solutions to a simplified magneto-viscoelastic flow system in three-dimensional space. This model couples the incompressible Navier-Stokes equation for the fluid velocity field, an evolution equation for the deformation tensor, and a gradient flow equation for the magnetization vector. Furthermore, we prove that the one-dimensional space-time Hausdorff measure of the potential singular set of such suitable weak solutions is zero.

Key words: Suitable weak solution, Partial regularity, Magneto-viscoelastic flow, Hausdorff dimension