论文标题
3D Navier-Stokes方程，具有不变边界条件
3D Navier-Stokes Equations with Nonvanishing Boundary Condition
论文作者
论文摘要
本文研究了有界域$ω\ subset \ mathbb {r}^3 $中不可压缩的Navier-Stokes方程的强解决方案的存在和规律性，但要符合边界条件$（U \ CDOT \ cdot \ vec {n}）|在这里，$ \ vec {n} $表示边界$ \partialΩ$的正常向量，该方程由$ \ partial_t u =νδU-（U \ cdot \ nabla）U- \ \ nabla p + f $，具有初始条件$ | ____________ {t = 0} = u_o \ $ ud = $ n $ nabla p + f $ n $ n $ n.本文旨在确定边界条件为$（u \ cdot \ vec {n}）| _ {\ partialω} = 0 $时，确定本地时间强解决方案的存在和规律性。
This paper investigates the existence and regularity of strong solutions to the incompressible Navier-Stokes equations within a bounded domain $Ω\subset \mathbb{R}^3$, subject to the boundary condition $(u\cdot \vec{n})|_{\partial Ω}=0$. Here, $\vec{n}$ represents the normal vector to the boundary $\partialΩ$, and the equation is given by $\partial_t u = νΔu - (u \cdot \nabla) u - \nabla p + f$, with initial condition $u|_{t=0}=u_o\in H$ and the divergence constraint $div\,u = 0$. This paper aims to establish the existence and the regularity of local-in-time strong solutions when the boundary condition is $(u\cdot \vec{n})|_{\partial Ω}=0$.
