The weak solvability of the steady problem modelling the flow of a viscous incompressible heat-conductive fluid through the profile cascade

The paper aims to theoretically study the mathematical model of a steady flow of a heat-conductive incompressible viscous fluid through a spatially periodic plane profile cascade.

Reduction of the infinite periodical problem to one period. Leray-Schauder fixed point principle was used.

This study proves the existence of a weak solution for arbitrarily large given data (i.e. the inflow velocity and the acting specific body force).

The author proposed a special boundary condition on the outflow of the domain not only for the velocity and pressure but also for the temperature.

To the author’s knowledge, the problem has not been studied earlier. More detailed overview is given in the paper in the first part.