Existence and uniqueness of solutions to the backward 2D stochastic Navier-Stokes equations

P. Sundar and Hong Yin

Stochastic Processes and their Applications, 2009, vol. 119, issue 4, 1216-1234

Abstract: The backward two-dimensional stochastic Navier-Stokes equations (BSNSEs, for short) with suitable perturbations are studied in this paper, over bounded domains for incompressible fluid flow. A priori estimates for adapted solutions of the BSNSEs are obtained which reveal a pathwise L[infinity](H) bound on the solutions. The existence and uniqueness of solutions are proved by using a monotonicity argument for bounded terminal data. The continuity of the adapted solutions with respect to the terminal data is also established.

Keywords: Backward; stochastic; Navier-Stokes; equations; The; Ito; formula; Galerkin; approximation; Monotonicity (search for similar items in EconPapers)
Date: 2009
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