Identifier

etd-04102013-165948

Degree

Doctor of Philosophy (PhD)

Department

Mathematics

Document Type

Dissertation

Abstract

In this work, a Wentzell-Freidlin type large deviation principle is established for the two-dimensional stochastic Navier-Stokes equations (SNSE's) with nonlinear viscosities. We fi_x000C_rst prove the existence and uniqueness of solutions to the two-dimensionalstochastic Navier-Stokes equations with nonlinear viscosities using the martingale problem argument and the method of monotonicity. By the results of Varadhan and Bryc, the large deviation principle (LDP) is equivalent to the Laplace-Varadhan principle (LVP) if the underlying space is Polish. Then using the stochastic control and weak convergence approach developed by Budhiraja and Dupuis, the Laplace-Varadhan principle for solutions of stochastic Navier-Stokesequations is obtained in appropriate function spaces.

Date

2013

Document Availability at the Time of Submission

Release the entire work immediately for access worldwide.

Committee Chair

Sundar, Padmanabhan

DOI

10.31390/gradschool_dissertations.1558

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