Asymptotic analysis of the generalized convection problem

The averaging method is justified and the complete asymptotics of a solution periodic in time is constructed and justified for an evolutional system of partial differential equations with quickly oscillating in time junior terms, some of which are proportional to the frequency of oscillations. The considered system generalizes the well-known thermal liquid convection problem (in Oberdeck–Boussinesc approach) when a vessel with a liquid vibrates with high frequency.