Mármol, Macarena Gómez; Gallego, Francisco Ortegón Existence of solution to nonlinear elliptic systems arising in turbulence modelling. (English) Zbl 1023.76017 Math. Models Methods Appl. Sci. 10, No. 2, 247-260 (2000). 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. Cited in 4 Documents MSC: 76F60 \(k\)-\(\varepsilon\) modeling in turbulence 35Q35 PDEs in connection with fluid mechanics Keywords:\(k\)-epsilon model; regularity; positivity; nonlinear elliptic systems; two-equation turbulence model; existence; transport terms PDFBibTeX XMLCite \textit{M. G. Mármol} and \textit{F. O. Gallego}, Math. Models Methods Appl. Sci. 10, No. 2, 247--260 (2000; Zbl 1023.76017) Full Text: DOI 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) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.