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Title: Local-in-time existence of a free-surface 3D Euler flow with H 2+δ initial vorticity in a neighborhood of the free boundary
Abstract

We consider the three-dimensional Euler equations in a domain with a free boundary with no surface tension. We assume thatu0H2.5+δis such thatcurlu0H2+δin an arbitrarily small neighborhood of the free boundary, and we use the Lagrangian approach to derive an a priori estimate that can be used to prove local-in-time existence and uniqueness of solutions under the Rayleigh–Taylor stability condition.

 
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Award ID(s):
1907992 2205493
PAR ID:
10471757
Author(s) / Creator(s):
;
Publisher / Repository:
IOP Publishing
Date Published:
Journal Name:
Nonlinearity
Volume:
36
Issue:
1
ISSN:
0951-7715
Page Range / eLocation ID:
636 to 652
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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