TY - JOUR
T1 - Analyticity of solutions for randomly forced two-dimensional Navier-Stokes equations
AU - Shirikyan, A.
PY - 2002/7
Y1 - 2002/7
N2 - A study is made of randomly forced two-dimensional Navier-Stokes equations with periodic boundary conditions. Under the assumption that the random forcing is analytic in the spatial variables and is a white noise in the time, it is proved that a large class of solutions, which contains all stationary solutions with finite energy, admits analytic continuation to a small complex neighbourhood of the torus. Moreover, a lower bound is obtained for the radius of analyticity in terms of the viscosity v, and it is shown that the Kolmogorov dissipation scale can be asymptotically estimated below by v2+d for any d > 0.
AB - A study is made of randomly forced two-dimensional Navier-Stokes equations with periodic boundary conditions. Under the assumption that the random forcing is analytic in the spatial variables and is a white noise in the time, it is proved that a large class of solutions, which contains all stationary solutions with finite energy, admits analytic continuation to a small complex neighbourhood of the torus. Moreover, a lower bound is obtained for the radius of analyticity in terms of the viscosity v, and it is shown that the Kolmogorov dissipation scale can be asymptotically estimated below by v2+d for any d > 0.
UR - http://www.scopus.com/inward/record.url?scp=0036664245&partnerID=8YFLogxK
U2 - 10.1070/RM2002v057n04ABEH000536
DO - 10.1070/RM2002v057n04ABEH000536
M3 - Article
SN - 0036-0279
VL - 57
SP - 785
EP - 799
JO - Uspekhi Matematicheskikh Nauk
JF - Uspekhi Matematicheskikh Nauk
IS - 4
ER -