Differential and Integral Equations

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

Pitágoras Pinheiro de Carvalho and Enrique Fernández-Cara

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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

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

First available in Project Euclid: 25 September 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35K60: Nonlinear initial value problems for linear parabolic equations 35Q30: Navier-Stokes equations [See also 76D05, 76D07, 76N10] 35Q35: PDEs in connection with fluid mechanics 76D05: Navier-Stokes equations [See also 35Q30] 76F30: Renormalization and other field-theoretical methods [See also 81T99] 80A22: Stefan problems, phase changes, etc. [See also 74Nxx]


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

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