The Library
Energy conservation for the Euler equations on T2 x R+ for weak solutions defined without reference to the pressure
Tools
Robinson, James C., Rodrigo, Jose L. and Skipper, Jack (2018) Energy conservation for the Euler equations on T2 x R+ for weak solutions defined without reference to the pressure. Asymptotic Analysis, 110 (3-4). pp. 185-202. doi:10.3233/ASY-181482 ISSN 0921-7134.
|
PDF
WRAP-energy-conservation-Euler-equations-Robinson-2018.pdf - Accepted Version - Requires a PDF viewer. Download (566Kb) | Preview |
Official URL: http://doi.org/10.3233/ASY-181482
Abstract
We study weak solutions of the incompressible Euler equations on T2×R+; we use test functions that are divergence free and have zero normal component, thereby obtaining a definition that does not involve the pressure. We prove energy conservation under the assumptions that u∈L3(0,T;L3(T2×R+)), lim|y|→01|y|∫0T∫T2∫x3>|y|∞|u(x+y)−u(x)|3dxdt=0, and an additional continuity condition near the boundary: for some δ>0 we require u∈L3(0,T;C0(T2×[0,δ])). We note that all our conditions are satisfied whenever u(x,t)∈Cα, for some α>1/3, with Hölder constant C(x,t)∈L3(T2×R+×(0,T)).
Item Type: | Journal Article | ||||||
---|---|---|---|---|---|---|---|
Subjects: | Q Science > QC Physics | ||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
Library of Congress Subject Headings (LCSH): | Fluid dynamics -- Mathematical models | ||||||
Journal or Publication Title: | Asymptotic Analysis | ||||||
Publisher: | I O S Press | ||||||
ISSN: | 0921-7134 | ||||||
Official Date: | 19 November 2018 | ||||||
Dates: |
|
||||||
Volume: | 110 | ||||||
Number: | 3-4 | ||||||
Page Range: | pp. 185-202 | ||||||
DOI: | 10.3233/ASY-181482 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||
Copyright Holders: | IOS Press | ||||||
Date of first compliant deposit: | 4 July 2018 | ||||||
Date of first compliant Open Access: | 23 April 2019 | ||||||
Related URLs: |
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |
Downloads
Downloads per month over past year