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The mathematical analysis of the coupling of a turbulent kinetic energy equation to the Navier-Stokes equation with an eddy viscosity. (English) Zbl 0863.35077
The aim of this paper is to study the system consisting of Navier-Stokes equation and energy equation for an incompressible fluid, considered in a bounded domain in n (n=2,3), with homogeneous Dirichlet boundary conditions. In the case of bounded eddy viscosity, first, one proves that the system has weak solutions in the steady-state case and in the bidimensional evolution case. Then, existence of weak solutions is obtained when the energy equation is coupled to the three-dimensional evolution Stokes equation. Finally, the regularity of the solutions and the problem of passing to the limit in the equations are considered.
Reviewer: V.A.Sava (Iaşi)

MSC:
35Q30Stokes and Navier-Stokes equations
76F05Isotropic turbulence; homogeneous turbulence
35D05Existence of generalized solutions of PDE (MSC2000)