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The Quarterly Journal of Mechanics and Applied Mathematics 1986 39(1):15-24; doi:10.1093/qjmam/39.1.15
© 1986 by Oxford University Press
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EXISTENCE AND NON-UNIQUENESS OF SIMILARITY SOLUTIONS OF A BOUNDARY-LAYER PROBLEM

M. Y. HUSSAINI and W. D. LAKIN

( Institute for Computer Applications in Science and Engineering, NASA Langley Research Center Hampton, VA 23665, USA
Department of Mathematical Sciences, Old Dominion University Norfolk, VA 23508, USA )

This work considers a Blasius boundary-value problem with inhomogeneous lower-boundary conditions f(0) = 0 and f'(0) = –{lambda} with {lambda} strictly positive. The Crocco-variable formulation of this problem has a key term which changes sign in the interval of interest. It is shown that solutions of the boundary-value problem do not exist for values of {lambda} larger than a positive critical value {lambda}*. The existence of solutions is proved for 0<{lambda}≤{lambda}* by considering an equivalent initial-value problem. However, for 0<{lambda}<{lambda}*, solutions of the boundary-value problem are found to be non-unique. Physically, this non-uniqueness is related to multiple values of the skin friction.


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