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On the existence of solution of the Greenspan-Carrier equation

Published online by Cambridge University Press:  09 April 2009

H. P. Heinig
Affiliation:
Department of MathematicsMcMaster University Hamilton, Ontario, Canada
K. Kuen Tam
Affiliation:
Department of MathematicsMcGill University Montreal, Quebec, Canada
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We are concerned with the flow of a viscous incompressible electrically conducting fluid of constant properties past a semi-infinite rigid plate. The governing boundary layer equations were derived by Greenspan and Carrier [2] in 1959. Numerical solutions of these equations subject to different boundary conditions have been considered by Stewartson and Wilson [5], Wilson [8], and recently by Bramley [1].

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1973

References

[1]Bramely, J. S., ‘Further investigation of the dual solutions of the Greenspan-Carrier equations’, Phys. Fluid 13, (1970), 13891391.CrossRefGoogle Scholar
[2]Greenspan, H. P., and Carrier., G. F., ‘The magnetohydrodynamic flow past a flat plate’, J. Fluid Mech. 6, (1959), 7796.CrossRefGoogle Scholar
[3]Reuter, G. E. H., and Stewartson, K., ‘A non-existence theorem in magneto fluid dynamics’, Physics of Fluids, 4 (1961) 276277.CrossRefGoogle Scholar
[4]Serrin, J. and McLeod, J. B., ‘The existence of similar solutions for some laminar boundary layer problems’, Arch. Rational Mech. Anal. 41 (1968), 288303.Google Scholar
[5]Stewartson, K. and Wilson, D. H., ‘Dual solutions of the Greenspan-Carrier equations II’, J. Fluid Mech. 18 (1964), 337–249.CrossRefGoogle Scholar
[6]Tam, K. K., ‘On the asymptotic solution of viscous incompressible flow past a heated paraboloid of revolution’, SIAM Journal App. Math. 20 (1971), 714721.CrossRefGoogle Scholar
[7]Weyl, H., ‘On the differential equations of the simplest boundary layer problems’, Ann. Math. 43 (1942), 381407.CrossRefGoogle Scholar
[8]Wilson, D. H., ‘Dual solutions of the Greenspan-Carrier equations’, J. Fluid Mech. 18 (1964), 161166.CrossRefGoogle Scholar