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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 N components of the velocity field u coupled with two scalar quantities θ and φ. 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 L1. Some existence results are shown in this paper, including L -estimates and positivity for both θ and φ.

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