Probabilistic estimates for the Two Dimensional Stochastic Navier-Stokes Equations

/ Authors

/ Abstract

W e considerthe N avier-Stokes equation on a two dim ensionaltoruswith a random force, white noise in tim e and analytic in space,for arbitrary Reynolds num ber R . W e prove probabilistic estim atesforthe long tim e behaviourofthe solutionsthatim ply boundsfor the dissipation scale and energy spectrum as R ! 1 .

Probabilistic estimates for the Two Dimensional Stochastic Navier-Stokes Equations

/ Authors

J.Bricmont, A.Kupiainen, R.Lefevere

/ Abstract

W e considerthe N avier-Stokes equation on a two dim ensionaltoruswith a random force, white noise in tim e and analytic in space,for arbitrary Reynolds num ber R . W e prove probabilistic estim atesforthe long tim e behaviourofthe solutionsthatim ply boundsfor the dissipation scale and energy spectrum as R ! 1 .