Mathematical Analysis of Turbulent Flows Through Permeable Media

In this chapter, we consider the one-equation k-epsilon model most used in the applications to describe turbulent flows through permeable media. The mathematical problem we study here is supplemented with no-slip boundary conditions and suitable initial conditions. For the associated boundary-value problem, we prove the existence of weak solutions for space dimensions 2 <= d <= 4. With respect to the original initial- and boundary-value problem, we prove the existence of suitable weak solutions in the space dimensions of physics interest.