# American Institute of Mathematical Sciences

## Global existence and exponential decay of strong solutions to the cauchy problem of 3D density-dependent Navier-Stokes equations with vacuum

 1 College of Mathematics, Changchun Normal University, Changchun 130032, China 2 Department of Mathematics, Nanjing University, Nanjing 210093, China

Received  May 2019 Published  May 2020

This paper deals with the 3D incompressible Navier-Stokes equations with density-dependent viscosity in the whole space. The global well-posedness and exponential decay of strong solutions is established in the vacuum cases, provided the assumption that the bound of density is suitably small, which extends the results of [Nonlinear Anal. Real World Appl., 46:58-81, 2019] to the global one. However, it's entirely different from the recent work [arxiv: 1709.05608v1, 2017] and [J. Math. Fluid Mech., 15:747-758, 2013], there is not any smallness condition on the velocity.

Citation: Yang Liu. Global existence and exponential decay of strong solutions to the cauchy problem of 3D density-dependent Navier-Stokes equations with vacuum. Discrete & Continuous Dynamical Systems - B, doi: 10.3934/dcdsb.2020163
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