Branching process associated with 2d-Navier Stokes equation | Zendy

Saïd Bénachour | Zendy; Bernard Roynette | Zendy; Pierre Vallois | Zendy

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Branching process associated with 2d-Navier Stokes equation

Author(s) -

Saïd Bénachour,

Bernard Roynette,

Pierre Vallois

Publication year - 2001

Publication title -

revista matemática iberoamericana

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.569

H-Index - 52

eISSN - 2235-0616

pISSN - 0213-2230

DOI - 10.4171/rmi/297

Subject(s) - branching (polymer chemistry) , branching process , process (computing) , mechanics , mathematics , statistical physics , computer science , physics , materials science , composite material , operating system

O being a bounded open set in R·, with regular boundary, we associate with Navier-Stokes equation in O where the velocity is null on ?O, a non-linear branching process (Yt, t = 0). More precisely: E?0(ah,Ytn) = a?,hn, for any test function h, where ? = rot u, u denotes the velocity solution of Navier-Stokes equation. The support of the random measure Yt increases or decreases in one unit when the underlying process hits ?O; this stochastic phenomenon corresponds to the creation-annihilation of vortex localized at the boundary of O.

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