| Issue |
EPL
Volume 84, Number 5, December 2008
|
|
|---|---|---|
| Article Number | 50006 | |
| Number of page(s) | 6 | |
| Section | General | |
| DOI | https://doi.org/10.1209/0295-5075/84/50006 | |
| Published online | 09 December 2008 | |
Spontaneous symmetry breaking and finite-time singularities in d-dimensional incompressible flows with fractional dissipation
1
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
Corresponding authors: Gandhi.Viswanathan@pq.cnpq.br viswanathan.tenkasi@gmail.com
Received:
2
August
2008
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
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