论文标题
3D外部域中密度依赖性粘度的粘度Navier-Stokes方程的全球强解决方案
Global Strong Solutions to Density-Dependent Viscosity Navier-Stokes Equations in 3D Exterior Domains
论文作者
论文摘要
在三维（3D）外部结构域中研究了具有密度依赖性粘度的非均匀Navier-Stokes方程。我们证明，只要初始速度的梯度很小，我们就会及时地存在强大的解决方案。在这里，初始密度被允许包含真空状态。此外，在开发了一些新技术和方法之后，还获得了具有指数衰减率的强溶液的大型溶液行为。
The nonhomogeneous Navier-Stokes equations with density-dependent viscosity is studied in three-dimensional (3D) exterior domains with nonslip or slip boundary conditions. We prove that the strong solutions exists globally in time provided that the gradient of the initial velocity is suitably small. Here the initial density is allowed to contain vacuum states. Moreover, after developing some new techniques and methods, the large-time behavior of the strong solutions with exponential decay-in-time rates is also obtained.
