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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Uniqueness for a stochastic inviscid dyadic model


Authors: D. Barbato, F. Flandoli and F. Morandin
Journal: Proc. Amer. Math. Soc. 138 (2010), 2607-2617
MSC (2010): Primary 60H15; Secondary 35Q31, 35R60, 76B03, 76M35
Published electronically: February 24, 2010
MathSciNet review: 2607891
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Abstract: For the deterministic dyadic model of turbulence, there are examples of initial conditions in $ l^{2}$ which have more than one solution. The aim of this paper is to prove that uniqueness, for all $ l^{2}$-initial conditions, is restored when a suitable multiplicative noise is introduced. The noise is formally energy preserving. Uniqueness is understood in the weak probabilistic sense.


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Additional Information

D. Barbato
Affiliation: Dipartimento di Matematica Pura e Applicata, Università di Padova, via Trieste, 63, 35121 Padova, Italy
Email: barbato@math.unipd.it

F. Flandoli
Affiliation: Dipartimento di Matematica Applicata, Università di Pisa, via Buonarroti, 1, 56127 Pisa, Italy
Email: flandoli@dma.unipi.it

F. Morandin
Affiliation: Dipartimento di Matematica, Università di Parma, viale G.P. Usberti, 53A, 43124 Parma, Italy
Email: francesco.morandin@unipr.it

DOI: http://dx.doi.org/10.1090/S0002-9939-10-10318-9
PII: S 0002-9939(10)10318-9
Received by editor(s): October 21, 2009
Published electronically: February 24, 2010
Additional Notes: This work was supported in part by the University of Padova under grant CPDA082105/08.
Communicated by: Edward C. Waymire
Article copyright: © Copyright 2010 American Mathematical Society