Volume 84, Number 5, December 2008
|Number of page(s)||6|
|Published online||09 December 2008|
Spontaneous symmetry breaking and finite-time singularities in d-dimensional incompressible flows with fractional dissipation
Consortium of the Americas for Interdisciplinary Science, University of New Mexico 800 Yale Blvd. NE, Albuquerque, NM 87131, USA
2 Instituto de Física, Universidade Federal de Alagoas - Maceió - AL, CEP 57072-970, Brazil
3 Universidade Federal de Alagoas - Maceió - AL, CEP 57072-970, Brazil
Accepted: 27 October 2008
We investigate the formation of singularities in incompressible flows governed by Navier-Stokes equations in d 2 dimensions with a fractional Laplacian . We derive analytically a sufficient but not necessary condition for the solutions to remain always smooth and show that finite-time singularities cannot form for . Moreover, initial singularities become unstable for . The scale invariance symmetry intrinsic to the Navier-Stokes system becomes spontaneously broken, except at the critical point .
PACS: 05.40.Fb – Random walks and Levy flights / 47.10.ad – Navier-Stokes equations / 05.70.Jk – Critical point phenomena
© EPLA, 2008
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.