For 3D inhomogeneous incompressible micropolar equations with power-law density-dependent transport coefficients, global strong solutions and exponential decay hold whenever the initial density is bounded below by a sufficiently large constant.
Global large strong solution of the 3D inhomogeneous Navier-Stokes equations with density-dependent viscosity
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abstract
This paper concerns the Dirichlet problem of three-dimensional inhomogeneous Navier-Stokes equations with density-dependent viscosity. When the viscosity coefficient $\mu(\rho)$ is a power function of the density ($\mu(\rho)=\mu\rho^\alpha$ with $\alpha>1$), it is proved that the system will admit a unique global strong solution as long as the initial data are sufficiently large. This is the first result concerning the existence of large strong solution for the inhomogeneous Navier-Stokes equations in three dimensions.
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Global well-posedness and exponential decay of strong solution for the three-dimensional inhomogeneous incompressible micropolar equations with density-dependent transport coefficients and large initial data
For 3D inhomogeneous incompressible micropolar equations with power-law density-dependent transport coefficients, global strong solutions and exponential decay hold whenever the initial density is bounded below by a sufficiently large constant.