The 3D Euler equations with inflow, outflow and vorticity boundary conditions
Abstract
The 3D incompressible Euler equations in a bounded domain are most often supplemented with impermeable boundary conditions, which constrain the fluid to neither enter nor leave the domain. We establish well-posedness with inflow, outflow of velocity when either the full value of the velocity is specified on inflow, or only the normal component is specified along with the vorticity (and an additional constraint). We derive compatibility conditions to obtain regularity in a H\"{o}lder space with prescribed arbitrary index, and allow multiply connected domains. Our results apply as well to impermeable boundaries, establishing higher regularity of solutions in H\"{o}lder spaces.
Keywords
Cite
@article{arxiv.2203.15180,
title = {The 3D Euler equations with inflow, outflow and vorticity boundary conditions},
author = {Gung-Min Gie and James P. Kelliher and Anna L. Mazzucato},
journal= {arXiv preprint arXiv:2203.15180},
year = {2024}
}
Comments
Several corrections made, in particular, the definitions of functions spaces in which solutions lie