Coupling the Stokes and Navier-Stokes equations with two scalar nonlinear parabolic equations
This work deals with a system of nonlinear parabolic equations arising in turbulence modelling. The unknowns are the N components of the velocity field u coupled with two scalar quantities θ and φ. The system presents nonlinear turbulent viscosity and nonlinear source terms of the form and lying in L1. Some existence results are shown in this paper, including -estimates and positivity for both θ and φ.