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.

中文翻译：

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具有真空的3D依赖密度的Navier-Stokes方程的柯西问题的强解的整体存在和指数衰减

本文研究了在整个空间中密度依赖粘度的3D不可压缩Navier-Stokes方程。在真空情况下，建立了强解的整体适定性和指数衰减，条件是假设密度的边界适当小，从而扩展了[非线性分析的结果]。Real World Appl。，46：58-81，2019]移至全球。但是，它与最近的工作[arxiv：1709.05608v1，2017]和[J. 数学。Fluid Mech。，15：747-758，2013]，速度上没有任何细微的条件。