Global well-posedness and exponential decay of strong solutions for 2D nonhomogeneous Magneto-Micropolar equations with density-dependent viscosity

Abstract We study an initial boundary value problem of 2D nonhomogeneous magneto-micropolar equations with density-dependent viscosity in smooth bounded domains. When the initial density can contain vacuum states, we prove that there is a unique global strong solution for the system under the assumption that initial velocity is suitably small. In particular, the initial data can be arbitrarily large except the gradient of velocity. Finally, we obtain the exponential decay rates of strong solutions by using the energy method. MSC(2010). 35Q35, 76D03.