Existence and nonuniqueness of similarity solutions of a boundarylayer problem
Abstract
A Blasius boundary value problem with inhomogeneous lower boundary conditions f(0) = 0 and f'(0) =  lambda with lambda strictly positive was considered. 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 proven for 0 lambda lambda by considering an equivalent initial value problem. It is found however that for 0 lambda lambda, solutions of the boundary value problem are nonunique. Physically, this nonuniqueness is related to multiple values of the skin friction.
 Publication:

Quarterly Journal of Mechanics and Applied Mathematics
 Pub Date:
 February 1986
 Bibcode:
 1986QJMAM..39...15H
 Keywords:

 Blasius Equation;
 Boundary Layers;
 Complex Variables;
 Crocco Method;
 Uniqueness Theorem;
 Boundary Conditions;
 Differential Equations;
 Similarity Theorem;
 Singularity (Mathematics);
 Fluid Mechanics and Heat Transfer