On Prandtl's turbulence model: Existence of weak solutions to the equations of stationary turbulent pipe-flow
Joachim Naumann, Jörg Wolf · Discrete and Continuous Dynamical Systems - S · 2013
Starting from Prandtl's (1945) turbulence model, we consider twosystems of PDEs for the scalar functions $u$ and $k$ which characterize the stationary turbulentpipe-flow. This system is completed by a homogeneous Dirichlet condition on $u$,and homogeneuos Neumann or mixed boundary conditions on $k$, respectively.For these boundary value problems we prove the existence of weak solutions $(u,k)$such that $k>0$ on a set of positive measure.