TY - JOUR
T1 - Random kick-forced 3D Navier-Stokes equations in a thin domain
AU - Chueshov, Igor
AU - Kuksin, Sergei
PY - 2008/4
Y1 - 2008/4
N2 - We consider the Navier-Stokes equations in the thin 3D domain 2 × (0, e), where 2 is a two-dimensional torus. The equation is perturbed by a non-degenerate random kick force. We establish that, firstly, when e ? 1, the equation has a unique stationary measure and, secondly, after averaging in the thin direction this measure converges (as e ? 0) to a unique stationary measure for the Navier-Stokes equation on 2. Thus, the 2D Navier-Stokes equations on surfaces describe asymptotic in time, and limiting in e, statistical properties of 3D solutions in thin 3D domains. © 2007 Springer-Verlag.
AB - We consider the Navier-Stokes equations in the thin 3D domain 2 × (0, e), where 2 is a two-dimensional torus. The equation is perturbed by a non-degenerate random kick force. We establish that, firstly, when e ? 1, the equation has a unique stationary measure and, secondly, after averaging in the thin direction this measure converges (as e ? 0) to a unique stationary measure for the Navier-Stokes equation on 2. Thus, the 2D Navier-Stokes equations on surfaces describe asymptotic in time, and limiting in e, statistical properties of 3D solutions in thin 3D domains. © 2007 Springer-Verlag.
UR - http://www.scopus.com/inward/record.url?scp=43149122237&partnerID=8YFLogxK
U2 - 10.1007/s00205-007-0068-2
DO - 10.1007/s00205-007-0068-2
M3 - Article
SN - 0003-9527
VL - 188
SP - 117
EP - 153
JO - Archive for Rational Mechanics and Analysis
JF - Archive for Rational Mechanics and Analysis
IS - 1
ER -