Question of Existence and Uniqueness of Solution for Navier-Stokes Equation with Linear 'Do-Nothing' Type Boundary Condition on the Outflow

摘要

The paper deals with the mathematical model of a flow of a viscous incompressible fluid through a 2D cascade of profiles. We consider a splited "do-nothing" type boundary condition on the outflow. The existence of a weak solution of a corresponding steady boundary value problem is known, see [2] and [3]. We recall the weak formulation, the theorem on existence and we study the uniqueness of the weak solution in this paper.