Three-Dimensional stochastic Navier-Stokes equations with Markov switching
Abstract
A finite-state Markov chain is introduced in the noise terms of the three-dimensional stochastic Navier-Stokes equations in order to allow for transitions between two types of multiplicative noises. We call such systems as stochastic Navier-Stokes equations with Markov switching. To solve such a system, a family of regularized stochastic systems is introduced. For each such regularized system, the existence of a unique strong solution (in the sense of stochastic analysis) is established by the method of martingale problems and pathwise uniqueness. The regularization is removed in the limit by obtaining a weakly convergent sequence from the family of regularized solutions, and identifying the limit as a solution of the three-dimensional stochastic Navier-Stokes equation with Markov switching.
Cite
@article{arxiv.2203.14442,
title = {Three-Dimensional stochastic Navier-Stokes equations with Markov switching},
author = {Po-Han Hsu and Padmanabhan Sundar},
journal= {arXiv preprint arXiv:2203.14442},
year = {2022}
}