Global Well-Posedness and exponential decay of 3D nonhomogeneous Navier-Stokes and magnetohydrodynamic equations with density-dependent viscosity and vacuum
Year: 2025
Type: conference-paper
Abstract: We establish the global well-posedness of strong solutions for the inhomogeneous magnetohydrodynamic equations with density-dependent viscosity in three-dimensional bounded domains, where the initial density is permitted to vanish. By skillfully employing various inequalities and scaling techniques, we demonstrate the existence and uniqueness of a global strong solution provided that ||σ(ρ 0)|| Lq is suitably small. Furthermore, we derive exponential decay rates for the solution. Importantly, no compatibility conditions need to be imposed on the initial data, even when vacuum states are present.
Author: Xiang Tang
Institution: Chongqing Jiaotong University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4408039442