The existence of global weak solutions for a multi-component plane flow

We consider the dynamics of multi-component heat-conducting viscous incompressible flow in a plane domain when the viscosity and thermal conductivity of the medium depend on temperature. The dynamics of the flow is governed by an initialboundary value problem for the Navier–Stokes system with heat conduction and heat transfer taken into account. The existence of a generalized global solution with velocity field and temperature of Hopfʹs class has been established in conjunction with the estimate of fractional smoothness of the order 1/2 in the time variable.