A sufficient condition for the Hamiltonian evolution
We give a sufficient condition for the time evolution of a finite quantum system to be a Hamiltonian one. We use the semigroup formalism recently developed by Kossakowski, Gorini, Sudarshan et al.
The main objective of this article is to study dynamic of the ::: three-dimensional Boussinesq equations with the periodic boundary ::: condition.We prove that when the Rayleigh number $R$ crosses the ::: first critical Rayleigh number $R_c$, the Rayleigh-Benard problem ::: bifurcates from the basic state to an global attractor $\Sigma$, which is homeomorphic to $S^3$.