The Library
Decay of weak solutions and the singular set of the three-dimensional Navier-Stokes equations
Tools
Robinson, James C. and Sadowski, Witold (2007) Decay of weak solutions and the singular set of the three-dimensional Navier-Stokes equations. Nonlinearity, Vol.20 (No.5). pp. 1185-1191. doi:10.1088/0951-7715/20/5/007 ISSN 0951-7715.
Research output not available from this repository.
Request-a-Copy directly from author or use local Library Get it For Me service.
Official URL: http://dx.doi.org/10.1088/0951-7715/20/5/007
Abstract
We consider the behaviour of weak solutions of the unforced three-dimensional Navier-Stokes equations, under the assumption that the initial condition has finite energy ( parallel to u parallel to(2) = integral vertical bar u vertical bar(2)) but in. nite enstrophy ( parallel to Du parallel to(2) = integral vertical bar curl u vertical bar(2)). We show that this has to be reflected in the solution for small times, so that in particular parallel to Du( t)parallel to -> +infinity as t -> 0. We also give some limitations on this 'backwards blow-up', and give an elementary proof that the upper box-counting dimension of the set of singular times can be no larger than one half. Although similar in flavour, this final result neither implies, nor is implied by, Scheffer's result that the 1/2-dimensional Hausdorff measure of the singular set is zero.
Item Type: | Journal Article | ||||
---|---|---|---|---|---|
Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Nonlinearity | ||||
Publisher: | Institute of Physics Publishing Ltd. | ||||
ISSN: | 0951-7715 | ||||
Official Date: | May 2007 | ||||
Dates: |
|
||||
Volume: | Vol.20 | ||||
Number: | No.5 | ||||
Number of Pages: | 7 | ||||
Page Range: | pp. 1185-1191 | ||||
DOI: | 10.1088/0951-7715/20/5/007 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
Data sourced from Thomson Reuters' Web of Knowledge
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |