Group analysis and exact solutions to the equations of microconvection (Q2760706)

The group classification is studied for a new model of convection under low gravity proposed by \textit{V. V. Pukhnachev} in [Model. Mekh. 6, No. 4, 47-56 (1992)] which is based on using the exact equations of continuity and momentum.NEWLINENEWLINENEWLINEFirst, for finding a group classification, the author investigates invariance properties of the model under consideration and, as a result, constructs a basis of admissible transformations.NEWLINENEWLINENEWLINENext, the author studies the problem of constructing optimal systems of first-order (\(\Theta_1\)) and second-order (\(\Theta_2\)) subalgebras of the Lie algebra of operators and exposes tables in which the operators of optimal systems of the subalgebras \(\Theta_1\) and \(\Theta_2\) are presented. Using these operators, the author constructs factor systems that make it possible to find certain exact solutions to the model.