REGARDING SOME PROBLEMS OF THE KUTTA-JOUKOVSKII CONDITION IN LIFTING SURFACE THEORY

We are interested in finding the velocity distribution at the wings of an aeroplane. Within the scope of a three-dimensional linear theory w e analyse a model which is formulated as a mixed screen boundary value problem for the Helmholtz equation (Delta + k(2))Phi = 0 in R(3)\(S) over bar where Phi denotes the perturbation velocity potential, induce d by the presence of the wings and (S) over bar = (L) over bar boolean OR (W) over bar with the projection L of the wings onto the (x, y)-pl ane and the wake W. Not all Cauchy data are given explicitly on L, res pectively W. These missing Cauchy data depend on the wing circulation Gamma. Gamma has to be fixed by the Kutta-Joukovskii condition: del Ph i should be finite near the trailing edge x(t) of L. To fulfil this co ndition in a way that all appearing terms can be defined mathematicall y exactly and belong to spaces which are physically meaningful, we pro pose to Ex Gamma by the condition of vanishing stress intensity factor s of Phi near x(t) up to a certain order such that del Phi\(xt) is an element of W-2(epsilon)(x(t)) subset of L(2)(x(t)), epsilon > 0. In th e two - dimensional case, and if L is the left half-plane in R(2), we have an explicit formula to calculate Gamma and we can control the reg ularity of Gamma and Phi.