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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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