| Full text | |
| Author(s): |
Bardos, C.
[1]
;
Lopes Filho, M. C.
[2]
;
Niu, Dongjuan
[3]
;
Nussenzveig Lopes, H. J.
[2]
;
Titi, E. S.
[4, 5, 6]
Total Authors: 5
|
| Affiliation: | [1] Univ Paris 07, Lab J L Lions, F-75009 Paris - France
[2] Univ Fed Rio de Janeiro, Inst Matemat, Dept Matemat Aplicada, BR-21941909 Rio De Janeiro, RJ - Brazil
[3] Capital Normal Univ, Sch Math Sci, Beijing 100048 - Peoples R China
[4] Univ Calif Irvine, Dept Mech & Aerosp Engn, Dept Math, Irvine, CA 92697 - USA
[5] Weizmann Inst Sci, Dept Comp Sci & Appl Math, IL-76100 Rehovot - Israel
[6] Tech Univ Darmstadt, CSI, Darmstadt - Germany
Total Affiliations: 6
|
| Document type: | Journal article |
| Source: | SIAM JOURNAL ON MATHEMATICAL ANALYSIS; v. 45, n. 3, p. 1871-1885, 2013. |
| Web of Science Citations: | 20 |
| Abstract | |
In this article we consider weak solutions of the three-dimensional incompressible fluid flow equations with initial data admitting a one-dimensional symmetry group. We examine both the viscous and inviscid cases. For the case of viscous flows, we prove that Leray-Hopf weak solutions of the three-dimensional Navier-Stokes equations preserve initially imposed symmetry and that such symmetric flows are stable under general three-dimensional perturbations, globally in time. We work in three different contexts: two-and-a-half-dimensional, helical, and axisymmetric flows. In the inviscid case, we observe that as a consequence of recent work by De Lellis and Szekelyhidi, there are genuinely three-dimensional weak solutions of the Euler equations with two-dimensional initial data. We also present two partial results where restrictions on the set of initial data and on the set of admissible solutions rule out spontaneous symmetry breaking; one is due to P.-L. Lions and the other is a consequence of our viscous stability result. (AU) | |
| FAPESP's process: | 07/51490-7 - Mathematical aspects of incompressible fluid dynamics |
| Grantee: | Milton da Costa Lopes Filho |
| Support Opportunities: | Research Projects - Thematic Grants |