Navier-Stokes equation and forward-backward stochastic differential system in the Besov spaces

2013/05/03 by Xin Chen, Chen, Xin, Ana Bela Cruzeiro +3
Mathematics · #35Q30 #60H30 #76D05 #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR) #math.AP #math.PR #msc:35Q30 #msc:60H30 #msc:76D05

paper · pdf · doi:10.48550/arxiv.1305.0647

43 pages

arxiv created 2013/05/28 · arxiv updated 2013/05/29

Abstract

The Navier-Stokes equation on Rd (d greater or equal to 3) formulated on Besov spaces is considered. Using a stochastic forward-backward differential system, the local existence of a unique solution in B_ r, with r > 1 + d is obtained. We also show p,p p the convergence to solutions of the Euler equation when the viscosity tends to zero. Moreover, we prove the local existence of a unique solution in B_ pr,q, with p > 1, 1 greater or equal to q greater or equal to infinity, r > max(1, d); here the maximal time interval depends on p the viscosity.

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