The aim of this paper is to prove the existence of a weak-renormalized solution to a simplified model of turbulence of the $k-\varepsilon$ kind in spatial dimension $N=2$. The unknowns are the average velocity field and pressure, the mean turbulent kinetic energy and an appropriate time dependent variable. The motion equation and the additional PDE are respectively solved in the weak and renormalized senses.

中文翻译：

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简化的$ k- \ varepsilon $湍流模型的弱重归一化解

本文的目的是证明在空间维$ N = 2 $中，$ k- \ varepsilon $类型的湍流简化模型具有弱重整化解决方案。未知数是平均速度场和压力，平均湍动能以及适当的时间相关变量。运动方程和附加PDE分别在弱和重新归一化的意义上求解。