2D Navier-Stokes equation with cylindrical fractional Brownian noise

Author(s)

Ferrario, Benedetta ^[1] ; Olivera, Christian ^[2]

Affiliation

^[1] Univ Pavia, Dipartimento Matemat F Casorati, Pavia - Italy

^[2] Univ Estadual Campinas, Dept Matemat, Campinas, SP - Brazil

• Document type: Journal article
• Source: Annali di Matematica Pura ed Applicata; v. 198, n. 3, p. 1041-1067, JUN 2019.
• Web of Science Citations: 0

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= , we prove a local existence and uniqueness result when and a global existence and uniqueness result when 1/2 < H < 1. (AU)

• FAPESP's process: 15/07278-0 - Stochastic dynamics: analytical and geometrical aspects with applications
• Grantee: Paulo Regis Caron Ruffino
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 17/17670-0 - Stochastic Partial Differential Equations and Particle Systems
• Grantee: Christian Horacio Olivera
• Support Opportunities: Regular Research Grants