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

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  • Sundar, P.
  • Yin, Hong

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.

Suggested Citation

  • Sundar, P. & Yin, Hong, 2009. "Existence and uniqueness of solutions to the backward 2D stochastic Navier-Stokes equations," Stochastic Processes and their Applications, Elsevier, vol. 119(4), pages 1216-1234, April.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:4:p:1216-1234
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    References listed on IDEAS

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    1. Sritharan, S.S. & Sundar, P., 2006. "Large deviations for the two-dimensional Navier-Stokes equations with multiplicative noise," Stochastic Processes and their Applications, Elsevier, vol. 116(11), pages 1636-1659, November.
    2. Ma, Jin & Yong, Jiongmin, 1997. "Adapted solution of a degenerate backward spde, with applications," Stochastic Processes and their Applications, Elsevier, vol. 70(1), pages 59-84, October.
    3. Rong, Situ, 1997. "On solutions of backward stochastic differential equations with jumps and applications," Stochastic Processes and their Applications, Elsevier, vol. 66(2), pages 209-236, March.
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