## Differential and Integral Equations

### Weak-renormalized solutions for a simplified $k-\varepsilon$ model of turbulence

#### Abstract

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.

#### Article information

Source
Differential Integral Equations, Volume 31, Number 11/12 (2018), 893-908.

Dates
First available in Project Euclid: 25 September 2018

Carvalho, Pitágoras Pinheiro de; Fernández-Cara, Enrique. Weak-renormalized solutions for a simplified $k-\varepsilon$ model of turbulence. Differential Integral Equations 31 (2018), no. 11/12, 893--908. https://projecteuclid.org/euclid.die/1537840875