We consider the Navier–Stokes equation on the 2D torus, with a stochastic forcing term which is a cylindrical fractional Wiener noise of Hurst parameter H . Following Albeverio and Ferrario (Ann Probab 32(2):1632–1649, 2004) and Da Prato and Debussche (J Funct Anal 196(1):180–210, 2002) which dealt with the case H = 1/2 , we prove a local existence and uniqueness result when 7/16< H < 1/2 and a global existence and uniqueness result when 1/2 < H < 1.
2D Navier–Stokes equation with cylindrical fractional Brownian noise
Ferrario B.
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2019-01-01
Abstract
We consider the Navier–Stokes equation on the 2D torus, with a stochastic forcing term which is a cylindrical fractional Wiener noise of Hurst parameter H . Following Albeverio and Ferrario (Ann Probab 32(2):1632–1649, 2004) and Da Prato and Debussche (J Funct Anal 196(1):180–210, 2002) which dealt with the case H = 1/2 , we prove a local existence and uniqueness result when 7/16< H < 1/2 and a global existence and uniqueness result when 1/2 < H < 1.File in questo prodotto:
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