The exponential behavior and stability of the stochastic three-dimensional primitive equations driven by Lévy noise

Abstract

This paper establishes the exponential behavior and stability of the stochastic three-dimensional primitive equations driven by Lévy noise via Burkholder–Davis–Gundy inequality and Itô formula. In particular, we prove that under some conditions on the forcing terms, the weak solution converges exponentially in the mean square and almost surely exponentially to the stationary solution.