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Existence of solution to nonlinear elliptic systems arising in turbulence modelling. (English) Zbl 1023.76017

Summary: We study nonlinear elliptic systems governing steady-state of a two-equation turbulence model derived from the so-called \(k-\varepsilon\) model. Two kinds of problems are considered: in the first one, we drop out transport terms, and we deduce the existence of a solution for \(N\geq 2\); in the second one we take into account all transport terms; in this case, the existence result holds for \(N=2\) or 3. Positivity and \(L^\infty\)-regularity of scalar quantities are also shown.

MSC:

76F60 \(k\)-\(\varepsilon\) modeling in turbulence
35Q35 PDEs in connection with fluid mechanics
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References:

[1] DOI: 10.1051/m2an:1999110 · Zbl 0921.76039 · doi:10.1051/m2an:1999110
[2] DOI: 10.1142/S0218202593000114 · Zbl 0773.76036 · doi:10.1142/S0218202593000114
[3] Simon J., Série pp 1167– (1993)
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