Showing papers in "Ima Journal of Applied Mathematics in 1981"

On boundary layers in fluid mechanics that decay algebraically along stretches of wall that are not vanishingly small

Abstract: It is shown that certain "backward" boundary layers exist which exhibit an algebraic behaviour near the outer edge, but which still predict the correct wall conditions along an extended part of the boundary. This seems to be in contradiction with common knowledge which has it that such boundary-layer solutions can apply only at singular points in the flow field. However, the paper shows that the very same methods that prove the limited applicability of "algebraic" boundary layers in forward flows (flows with a definite leading edge) can be used to ascertain the extended applicability of such solutions in "backward" flows (when the leading edge recedes to stations infinitely far upstream).

A bound for solutions of a fourth order dynamical system

Abstract: We consider the homogeneous linearised equation of yawing motion of a spinning projectile $$\xi '' + {\rm A}(s) \xi ' + B(s) \xi = 0$$ where A and B are complex functions of the real independent variable s It is shown that $$\left| {\xi (s)} \right| < \operatorname{Re} ^{ - \tfrac{1}{2}\int_0^s {\left\{ {\mathbb{R}(A(\eta )) + v(\eta )} \right\}d\eta } } $$ where R is a positive constant and ν(s) is a real function of s