论文标题
有限域中3D Navier-Stokes方程的解决方案的非唯一性
Non-uniqueness of solutions for 3D Navier-Stokes equations in bounded domains
论文作者
论文摘要
本文研究了有限域中不可压缩的3D Navier-Stokes方程的局部限时强度解决方案的独特性/非唯一性，该方程为$ \ partial_t u = v Nabla \ cdot \ nabla U- \ nabla U- \ nabla u- \ nabla p+ f $ and $ div〜u = 0 $。 这项研究的重点是将边界条件定义为$ u \ cdot \ vec {n} | _ {\partialΩ} = 0 $的情况。本文证明了在这种边界条件下的Navier-Stokes方程有两个不同的强解决方案。
This paper examines the uniqueness/non-uniqueness of local-in-time strong solutions for the incompressible 3D Navier-Stokes equations in bounded domains, which are $\partial_t u=νΔu- u\cdot \nabla u-\nabla p+ f$ and $div~u=0$. The focus of this study is on the case where the boundary condition is defined as $u\cdot \vec{n}|_{\partialΩ}=0$. This paper demonstrates the existence of two distinct strong solutions to the Navier-Stokes equations under this boundary condition.
