Analysis, dynamics, and applications seminar: Rongchang Liu

Title: Some recent studies on the stochastic primitive equations

 

Abstract: The system of primitive equations models large-scale oceanic and atmospheric dynamics and is derived from the Navier-Stokes equations by applying the hydrostatic approximation. In this talk, I will present recent studies on the behavior of this system under the influence of stochastic noise. Specifically, for the inviscid primitive equations, we demonstrate that suitable noise can restore local well-posedness and prevent finite-time blowups with high probability. For the fractionally dissipated primitive equations, which interpolate between the inviscid and viscous cases, we establish local well-posedness with transport noise. Lastly, for the viscous system with additive white noise, we show that in the large rotational limit, the long-term statistics are governed by the unique invariant measure of the limiting resonant system. These results are joint work with Ruimeng Hu (UCSB), Quyuan Lin (Clemson), and Vincent Martinez (CUNY).