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Coupling the Stokes and Navier–Stokes equations with two scalar nonlinear parabolic equations

Macarena Gómez Mármol;  Francisco Ortegón Gallego — 2010

ESAIM: Mathematical Modelling and Numerical Analysis

This work deals with a system of nonlinear parabolic equations arising in turbulence modelling. The unknowns are the components of the velocity field coupled with two scalar quantities and . The system presents nonlinear turbulent viscosity A ( θ , ϕ ) and nonlinear source terms of the form θ 2 | ∇ u | 2 and θ ϕ | ∇ u | 2 lying in . Some existence results are shown in this paper, including L ∞ -estimates and positivity for both and .

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