Dynamic of rotating fluid layers: $$L^2$$ L 2 -absorbing sets and onset of convection

Abstract

Via the longtime behavior of the perturbations to thermal conduction solution $$m_0$$ , the nonlinear longtime behavior of Navier–Stokes fluid mixtures filling horizontal rotating layers uniformly heated from below and salted by one salt—either from above or below—is investigated. Via the existence of $$L^2$$ -absorbing sets, it is shown that the perturbations to $$m_0$$ are ultimately bounded. The onset of steady or oscillatory convection is analyzed. Via a Linearization Principle (Rionero in Rend Lincei Mat Appl 25:1–44, 2014) it is shown that the linear theory captures completely the physics of the problem since the linear stability implies the nonlinear global asymptotic stability in the $$L^2$$ -norm.