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Coupling the Stokes and Navier-Stokes equations with two scalar nonlinear parabolic equations. (English) Zbl 0921.76039
Summary: 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 \(\theta\) and \(\varphi\). The system presents nonlinear turbulent viscosity \(A(\theta, \varphi)\) and nonlinear source terms of the form \(\theta^2|\nabla u|^2\) and \(\theta \varphi |\nabla u|^2\) lying in \(L^1\). Some existence results are shown in this paper, including \(L^\infty\)-estimates and positivity for both \(\theta\) and \(\varphi\).

MSC:
76D05 Navier-Stokes equations for incompressible viscous fluids
76D07 Stokes and related (Oseen, etc.) flows
35Q30 Navier-Stokes equations
76F10 Shear flows and turbulence
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