Coupled NavierStokes system
turbulent kinetic energy
bounded eddy viscosity
kepsilon modeling
On Existence and Regularity of Solutions for a Stationary
NavierStokes System Coupled to an Equation for the Turbulent
Kinetic Energy.
PierreEtienne Druet
Druet
PierreEtienne
Institut für Mathematik, HumboldtUniversität zu Berlin (ISSN 08630976),
On Existence and Regularity of Solutions for a Stationary
NavierStokes System Coupled to an Equation for the Turbulent
Kinetic Energy.
PierreEtienne Druet
Preprint series:
Institut für Mathematik, HumboldtUniversität zu Berlin (ISSN 08630976),
MSC 2000
 35D05 Existence of generalized solutions

35J60 Nonlinear PDE of elliptic type

76D05 NavierStokes equations

76F60 $k$$\varepsilon$ modeling
Abstract
We investigate a stationary model for turbulent flows, in which the NavierStokes system is coupled to an equation for the density of turbulent kinetic energy through a bounded coefficient of eddy viscosity. We prove the existence of weak solutions for which the gradients are higher integrable.
The latter property allows us to prove that the model is well posed in the two dimensional case, provided that the external forcing remains sufficiently small.
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