On the global well-posedness of 3D inhomogeneous incompressible Navier-Stokes system with density-dependent viscosity

Published 18 Jan 2024 in math.AP | (2401.09850v1)

Abstract: In this paper, we are concerned with the global well-posedness of 3D inhomogeneous incompressible Navier-Stokes equations with density-dependent viscosity when the initial velocity is sufficiently small in the critical Besov space $\dot{B}^{\frac 12}$. Compared with the previous result of Abidi and Zhang (Science China Mathematics 58 (6) (2015) 1129-1150), we remove the smallness assumption of the viscosity $\mu(\rho_0)-1$ in $L^{{\infty}$-norm.}