Robinson, James C., Sadowski, Witold and Sharples, Nicholas (2013) On the regularity of lagrangian trajectories corresponding to suitable weak solutions of the Navier–Stokes equations. In: IUTAM Symposium on Topological Fluid Dynamics II - Theory and Applications, Cambridge, UK, 23-27 July 2012. Published in: Procedia IUTAM, Volume 7 pp. 161-166. ISSN 2210-9838. doi:10.1016/j.piutam.2013.03.019

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Abstract

The putative singular set S in space-time of a suitable weak solution u of the 3D Navier-Stokes equations has box-counting dimension no greater than 5/3. This allows one to prove that almost all trajectories avoid S. Moreover, for each point x that does not belong to S, one can find a neighbourhood U of x such that the function u is continuous on U and space derivatives of u are bounded on every compact subset of U. It follows that almost all Lagrangian trajectories corresponding to u are C-1 functions of time (Robinson & Sadowski, Nonlinearity 2009). We recall the main idea of the proof, give examples that clarify in what sense the uniqueness of trajectories is considered, and make some comments on how this result might be improved.

Item Type:	Conference Item (Paper)
Divisions:	Faculty of Science > Mathematics
Journal or Publication Title:	Procedia IUTAM
Publisher:	Elsevier BV
ISSN:	2210-9838
Official Date:	2013
Dates:	Date Event 2013 Published
Volume:	Volume 7
Page Range:	pp. 161-166
DOI:	10.1016/j.piutam.2013.03.019
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Open Access
Conference Paper Type:	Paper
Title of Event:	IUTAM Symposium on Topological Fluid Dynamics II - Theory and Applications
Type of Event:	Other
Location of Event:	Cambridge, UK
Date(s) of Event:	23-27 July 2012

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