Vajravelu, K.; Cannon, J. R.; Rollins, D. Analytical and numerical solutions of nonlinear differential equations arising in non-Newtonian fluid flows. (English) Zbl 0974.34017 J. Math. Anal. Appl. 250, No. 1, 204-221 (2000). Using Schauder technique and a priori estimates, the authors study a boundary value problem for a nonlinear second-order ordinary differential equation which describes a rotational flow of a viscoelastic fluid around a circular cylinder. The authors prove existence and uniqueness results, and investigate the asymptotic behaviour of the solution as a material constant tends to zero. Finally, analytical results are compared with numerical solutions. Reviewer: Oleg Titow (Berlin) Cited in 1 ReviewCited in 3 Documents MSC: 34B15 Nonlinear boundary value problems for ordinary differential equations 76A10 Viscoelastic fluids 76U05 General theory of rotating fluids 34B30 Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) Keywords:Schauder technique; a priori estimates; boundary value problem; nonlinear second-order ordinary differential equation; rotational flow; viscoelastic fluid; circular cylinder; existence; uniqueness; asymptotic behaviour PDFBibTeX XMLCite \textit{K. Vajravelu} et al., J. Math. Anal. Appl. 250, No. 1, 204--221 (2000; Zbl 0974.34017) Full Text: DOI References: [1] Beard, D. W.; Walters, K., Elastico-viscous boundary layer flows, Proc. Cambridge Philos. Soc., 60, 667-674 (1964) · Zbl 0123.41601 [2] Garg, V. K.; Rajagopal, K. R., Flow of a non-Newtonian fluid past a wedge, Acta Mech., 88, 113-123 (1991) [3] Rajeswari, G. K.; Rathna, S. L., Flow of a particular class of non-Newtonian visco-elastic and visco-elastic fluids near a stagnation point, Z. Angew. Math. Phys., 13, 43-57 (1962) · Zbl 0105.19503 [4] Markovitz, H.; Coleman, B. D., Advances in Applied Mechanics (1964), Academic Press: Academic Press New York · Zbl 0133.19205 [5] Acrivos, A., A theoretical analysis of laminar natural convection heat transfer to non-Newtonian fluids, Amer. Inst. Chem. Engrg. J., 6, 584-590 (1960) [6] Dunn, J. E.; Rajagopal, K. R., Fluids of differential type: Critical review and thermodynamic analysis, Internat. J. Engrg. Sci., 33, 689-729 (1995) · Zbl 0899.76062 [7] Vajravelu, K.; Rollins, D., Heat transfer in a viscoelastic fluid over a stretching sheet, J. Math. Anal. Appl., 158, 241-255 (1991) · Zbl 0725.76019 [8] Sarma, M. S.; Rao, B. N., Heat transfer in a viscoelastic fluid over a stretching sheet, J. Math. Anal. Appl., 222, 268-275 (1998) · Zbl 0907.76006 [9] Troy, W. C.; Overman, E. A.; Ermentrout, G. B.; Keener, J. P., Uniqueness of flow of a second order fluid past a stretching sheet, Quart. Appl. Math., 44, 753-755 (1987) · Zbl 0613.76006 [10] Chang, W. D., The nonuniqueness of the flow of a viscoelastic fluid over a stretching sheet, Quart. Appl. Math., 47, 365-366 (1989) · Zbl 0683.76012 [11] Lawrence, P. S.; Rao, B. N., Reinvestigation of the nonuniqueness of the flow of a viscoelastic fluid over a stretching sheet, Quart. Appl. Math., 51, 401-404 (1993) · Zbl 0781.76006 [12] Chang, W. D.; Kazarinoff, N. D.; Lu, C., A new family of explicit solutions for the similarity equations modelling flow of a non-Newtonian fluid over a stretching sheet, Arch. Rational Mech. Anal., 113, 191-195 (1991) · Zbl 0723.76010 [13] Vajravelu, K.; Roper, T., Flow and heat transfer in a second grade fluid over a stretching sheet, Internat. J. Nonlinear Mech., 34, 1031-1036 (1999) · Zbl 1006.76005 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.