Doctor of Philosophy (PhD)
This dissertation is devoted to the study of three-dimensional (regularized) stochastic Navier-Stokes equations with Markov switching. A Markov chain is introduced into the noise term to capture the transitions from laminar to turbulent flow, and vice versa. The existence of the weak solution (in the sense of stochastic analysis) is shown by studying the martingale problem posed by it. This together with the pathwise uniqueness yields existence of the unique strong solution (in the sense of stochastic analysis). The existence and uniqueness of a stationary measure is established when the noise terms are additive and autonomous. Certain exit time estimates (exponential inequalities) for solutions to such switching equations are obtained, and its connection with its counterpart in the non-switching scenario is discussed.
Hsu, Po-Han, "Stochastic Navier-Stokes Equations with Markov Switching" (2021). LSU Doctoral Dissertations. 5472.