Global Solvability for 3D Incompressible Inhomogeneous Micropolar System in Critical Spaces

In this paper, we investigate the 3D inhomogeneous incompressible micropolar system with the initial density being discontinuous and the initial velocity possessing critical regularity. Assuming that is close to a positive constant, we obtain the global existence and uniqueness of the solution if is small in . The key ingredient in the proof lies in a new maximal regularity estimate for the generalized heat equation in Lorentz space. Our result corresponds to the interesting results established by Danchin and Wang [ Communications in Mathematical Physics , 2023] for 3D inhomogeneous incompressible Navier–Stokes equations. Besides, the uniqueness of the Fujita–Kato‐type solution for the micropolar fluids constructed by Qian, Chen, and Zhang [ Mathematische Annalen , 2023] is also established.