We study a simplified equation governing turbulent kinetic energy in a bounded domain, arising from turbulence modeling where the eddy diffusion is given by , with representing the Prandtl mixing length of the order of the distance to the boundary, and a right-hand side in . We obtain estimates of in spaces and we establish the convergence toward the formal limit equation in the sense of the distributions as goes to 0.

中文翻译：

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具有简并扩散和[公式省略]中的源项的非线性椭圆方程

我们研究了一个在有​​界域中控制湍流动能的简化方程，该方程源自湍流建模，其中涡流扩散由 给出，代表到边界的距离的普朗特混合长度，右侧为 。我们获得了空间中的估计，并在分布趋于 0 的意义上建立了向形式极限方程的收敛。