Title page for ETD etd-04122007-145924


Type of Document Dissertation
Author Yin, Hong
Author's Email Address yinhong@math.lsu.edu
URN etd-04122007-145924
Title Backward Stochastic Navier-Stokes Equations in Two Dimensions
Degree Doctor of Philosophy (Ph.D.)
Department Mathematics
Advisory Committee
Advisor Name Title
Padmanabhan Sundar Committee Chair
Ambar Sengupta Committee Member
Charles Neal Delzell Committee Member
Jimmie Lawson Committee Member
W. George Cochran Committee Member
Anitra WIlson Dean's Representative
Keywords
  • Backward stochastic Navier-Stokes equations
  • Lorenz system
  • Gronwall inequality
  • Truncated system
  • Galerkin approximation
Date of Defense 2007-04-09
Availability unrestricted
Abstract
There are two parts in this dissertation. The backward stochastic Lorenz system is studied in the first part. Suitable a priori estimates for adapted solutions of the backward stochastic Lorenz system are obtained. The existence and uniqueness of solutions is shown by the use of suitable truncations and approximations. The

continuity of the adapted solutions with respect to the terminal data is also established.

The backward stochastic Navier-Stokes equations (BSNSEs, for short) corresponding to incompressible fluid flow in a bounded domain $G$

are studied in the second part. Suitable a priori estimates for adapted solutions of the BSNSEs are obtained which reveal a surprising pathwise $L^{infty}(H)$ bound on the solutions. The existence of solutions is shown by using a monotonicity argument. Uniqueness is proved by using a novel method that uses finite-dimensional projections, linearization, and truncations. The continuity of the adapted solutions with respect to the terminal data and the external body force is also established.

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