Global well-posedness and exponential decay for 3D nonhomogeneous magneto-micropolar fluid equations with vacuum

Abstract

<p style='text-indent:20px;'>We consider an initial boundary value problem of three-dimensional (3D) nonhomogeneous magneto-micropolar fluid equations in a bounded simply connected smooth domain with homogeneous Dirichlet boundary conditions for the velocity and micro-rotational velocity and Navier-slip boundary condition for the magnetic field. We prove the global existence and exponential decay of strong solutions provided that some smallness condition holds true. Note that although the system degenerates near vacuum, there is no need to require compatibility conditions for the initial data via time weighted techniques.</p>

Global solvability to the 3D incompressible magneto-micropolar system with vacuum

“…Very recently, Zhong [22] considered the existence and exponential decay of global strong solutions to the 3D initial boundary problem of incompressible magnetomicropolar system with vacuum. However, the global existence of strong solution to the 3D Cauchy problem of ( 1)-( 2) with vacuum is not addressed.…”

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

“…Recently, With the help of Weighted function and the duality principle of BMO space and Hardy space, Zhong [19] investigated the global well-posedness to nonhomogeneous magneto-micropolar fluid equations with zero density at infinity in R 2 . Furthermore, for the homogeneous Dirichlet boundary conditions of the velocity and micro-rotational velocity and Navier-slip boundary condition of the magnetic field, he proved the initial boundary value problem of 3D nonhomogeneous magneto-micropolar fluid equations in [20]. The above results are all the density-independent viscosity.…”