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Title: The 3D Euler equations with inflow, outflow and vorticity boundary conditions
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 Hölder space with prescribed arbitrary index, and allow multiply connected domains. Our results apply as well to impermeable boundaries, establishing higher regularity of solutions in Hölder spaces.  more » « less
Award ID(s):
1909103 2206453
PAR ID:
10648640
Author(s) / Creator(s):
; ;
Publisher / Repository:
Elsevier
Date Published:
Journal Name:
Journal de mathématiques pures et appliquées
ISSN:
0021-7824
Subject(s) / Keyword(s):
Euler equations Boundary conditions Well-posedness Injection-suction
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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