In this paper, we prove the local well-posedness of strong solutions to the density-dependent incompressible magneto-micropolar system with vacuum. There is no assuming compatibility condition on the initial data.

We study the 3D compressible nematic liquid crystal flow in a bounded domain. We first prove a regularity criterion, and then use a bootstrap argument to prove the global well-posedness of strong solutions provided that $\|\rho _0\|_{L^\infty }+\|\nabla d

This paper proves the global well-posedness for the 2D Cahn-Hilliard-Boussinesq and a related system with partial viscous terms on bounded domains.

This paper proves a regularity criterion for the 3D generalized Hall-MHD system.