On an iterational method for the approximate solution of an initial- and boundary-value problem for the heat-convection equations (Q1324018)

An iterational method is proposed for finding the approximate solution of an initial- and boundary-value problem for a non-stationary quasilinear system governing the motion of a non-uniform heated viscous incompressible liquid. It is proved that the approximate solutions converge in the norm of the space \([W_ 2^{2,1}(Q)]^ n\times W_ 2^{2,1}(Q)\), and convergence-rate bounds are obtained. In the case of two space variables, the results are globally, and in the case of three, locally applicable.