Partial regularity of the solutions to a turbulent problem in porous media

Abstract

A one-equation turbulent model that is being used with success in the applications to model turbulent flows through porous media is studied in this work. We consider the classical Navier–Stokes equations, with feedback forces fields, coupled with the equation for the turbulent kinetic energy (TKE) through the turbulence production term and through the turbulent and the diffusion viscosities. Under suitable growth conditions on the feedback functions involved in the model, we prove the local higher integrability of the gradient solutions to the steady version of this problem.