A Nonlinear Elliptic Equation with a Degenerate Diffusion and a Source Term in L 1
Résumé
We study a simplified equation governing turbulent kinetic energy $k$ in a bounded domain, arising from turbulence modeling where the eddy diffusion is given by $\varrho(x) + \varepsilon$, with $\varrho$ representing the Prandtl mixing length of the order of the distance to the boundary, and a right-hand side in $L^1$. We obtain estimates of $\sqrt \varrho \g k$ in $L^q$ spaces and we establish the convergence toward the formal limit equation in the sense of the distributions as $\varepsilon$ goes to 0.
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