3D Navier-Stokes Equations with Nonvanishing Boundary Condition

Abstract

This paper investigates the existence and regularity of strong solutions to the incompressible Navier-Stokes equations within a bounded domain $\Omega \subset {\mathbb{R}}^3$, subject to the boundary condition $(u\cdot \vec{n}){|}_{\partial \Omega }=0$. Here, $\vec{n}$ represents the normal vector to the boundary $\partial \Omega$, and the equation is given by ${\partial }_{t}u=\nu \Delta u-(u\cdot \nabla )u-\nabla p+f$, with initial condition $u{|}_{t=0}=u_o\in H$ and the divergence constraint $divu=0$. This paper aims to establish the existence and the regularity of local-in-time strong solutions when the boundary condition is $(u\cdot \vec{n}){|}_{\partial \Omega }=0$.

arXiv commentarXiv admin note: text overlap with arXiv:2002.12765