# American Institute of Mathematical Sciences

October  2013, 6(5): 1371-1390. doi: 10.3934/dcdss.2013.6.1371

## On Prandtl's turbulence model: Existence of weak solutions to the equations of stationary turbulent pipe-flow

 1 Departement of Mathematics, Humboldt University Berlin, Unter den Linden 6, 10099 Berlin, Germany, Germany

Received  November 2011 Revised  March 2012 Published  March 2013

Starting from Prandtl's (1945) turbulence model, we consider two systems of PDEs for the scalar functions $u$ and $k$ which characterize the stationary turbulent pipe-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.
Citation: Joachim Naumann, Jörg Wolf. On Prandtl's turbulence model: Existence of weak solutions to the equations of stationary turbulent pipe-flow. Discrete & Continuous Dynamical Systems - S, 2013, 6 (5) : 1371-1390. doi: 10.3934/dcdss.2013.6.1371
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