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

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  • 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.
    Mathematics Subject Classification: Primary: 35J70, 76F02; Secondary: 35Q35, 76F25.

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