In the present project we will deal with the properties of the stationary and non-stationary problems, describing the heat-conducting viscous incompressible fluid flow in an open channel. Such problems represent the full system of the Navier-Stokes equations derived from the momentum conservation principle, heat equation and the continuity equation supplemented with the initial conditions and the so called mixed boundary conditions. We focus our attention especially on these problems: existence of solution of the stationary and non-stationary problems with the mixed boundary conditions on some neighborhood where the solution is known or for sufficiently small data of the problem, existence of solution of the non-stationary problem for arbitrary data on sufficiently short-time interval. Using the discrete stochastic least-action principle we derive a variational integrator for numerical solution of the non-steady full system of the Navier-Stokes equations. (en)
1. Důkaz existence řešení soustavy Navier-Stokesových rovnic pro teplo-vedoucí tekutinu s tzv. smíšenými okrajovými podmínkami: a) v blízkosti známého řešení b) na dost. malém časovém int. 2. Užitím diskrétního stochastického principu minimální akce odvodit variační integrátor pro numerické řešení.