Skip to content
Texas A&M University
Mathematics

Events for 04/27/2021 from all calendars

Nonlinear Partial Differential Equations

iCal  iCal

Time: 3:00PM - 4:00PM

Location: Zoom

Speaker: Yulia Klevtsova, Hydrometeorological Research Institute - Novosibirsk

Title: On the inviscid limit of stationary measures for the stochastic system of the Lorenz model describing a baroclinic atmosphere

Abstract: The talk is concerned with a nonlinear system of partial differential equations with parameters which describes the two-layer quasi-solenoidal Lorenz model for a baroclinic atmosphere on a rotating two-dimensional sphere. The right-hand side of the system is perturbed by white noise. It was obtained in the previous author's works the sufficient conditions on the right-hand side and the parameters for existence of a unique stationary measure of Markov semigroup defined by solutions of the Cauchy problem for this system, for the exponential convergence of the distributions of solutions to the stationary measure as t goes to infinity. In this work it was obtained the sufficient conditions on the right-hand side and the parameters for the existence a limiting point for any sequence of the stationary measures for this system when any sequence of the kinematic viscosity coefficients goes to zero. As it is well known, in practice, this coefficient is extremely small, so meteorologists are willing to replace it with zero. Is such a step justified? Until now, no such mathematical studies have been carried out for baroclinic models. This work is the first step in this direction. Additionally, a similar result was obtained for a simpler model of the atmosphere - the equation of a barotropic atmosphere.