Electron. J. Differential Equations, Vol. 2020 (2020), No. 05, pp. 1-18.

Solution to Navier-Stokes equations for turbulent channel flows

Jing Tian, Bingsheng Zhang

In this article, we continue the work done in [11] for turbulent channel flows described by the Navier-Stokes and the Navier-Stokes-alpha equations. We study non-stationary solutions in special function spaces. In particular, we show the term representing the sum of pressure and potential is harmonic in the space variable. We find an optimal choice for the function class.

Submitted August 2, 2019. Published January 10, 2020.
Math Subject Classifications: 35Q30, 35B41, 76D05.
Key Words: Navier-Stokes; Navier-Stokes-alpha; channel flow; turbulence.

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Jing Tian
Department of Mathematics
Towson University
Towson, MD 21252, USA
email: jtian@towson.edu
Bingsheng Zhang
Department of Mathematics
Texas A&M University
College Statoin, TX, 77843, USA
email: shanby84@gmail.com

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