Abstract
Analysis of a stochastic ocean model: Primitive Equations under location uncertainty
In this talk, I will present first the location uncertainty (LU) formalism, which allows to derive stochastic interpretations of physical conservation laws systematically (such as of mass, momentum and energy). This approach typically involves transport noises, which have been widely studied by the mathematical community. Next, the LU formalism will serve to interpret the primitive equations in the stochastic context. In particular, the arising interpretation allows to infer a relaxation of the classical hydrostatic balance through the noise. Due to the new stochastic non-hydrostatic terms, well-posedness appears significantly more intricate to study, therefore these terms will be regularised using a low-pass filter. The proof of pathwise global existence and uniqueness will be presented breifly in this context.
Eventually, I will discuss the link between the LU relaxed primitive and the 3D LU Navier-Stokes equations. Namely the aforementioned stochastic non-hydrostatic terms can be formally recovered from the Navier-Stokes equations, using a specific noise scaling. Moreover, I will present a few error estimates that establish the convergence of the 3D LU Navier-Stokes towards the LU primitive equations in the limit of vanishing aspect ratio.