Regularity and uniqueness for the stationary large eddy simulation model

In the note we are concerned with higher regularity and uniqueness of solutions to the stationary problem arising from the large eddy simulation of turbulent ows. The system of equations contains a nonlocal nonlinear term, which prevents straightforward application of a difference quotients method. The existence of weak solutions was shown in A. Świerczewska: Large eddy simulation. Existence of stationary solutions to the dynamical model, ZAMM, Z. Angew. Math. Mech. 85 (2005), 593–604 and P. Gwiazda, A. Świerczewska: Large eddy simulation turbulence model with Young measures, Appl. Math. Lett. 18 (2005), 923–929.