A steady flow through a plane cascade of profiles with an arbitrarily large inflow_The mathematical model, existence of a weak solution

The paper deals with a mathematical model of a viscous stationary incompressible flow through a cascade of profiles. The problem for the Navier-Stokes system is formulated in a domain corresponding to one spatial period of the cascade. We consider several types of boundary conditions on various parts of the boundary (the inflow, the artificial lower and upper boundaries, the profile, the outflow). We solve the problem with an arbitrarily large inflow into the turbine. We formulate the “artificial” boundary condition on the outflow (the modification of the so called do-nothing condition) which enables us to prove the existence of a weak solution for any inflow.