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 we analyse a model which is formulated as a mixed screen boundary value problem for the Helmholtz equation (Δ + k 2 )Φ = 0 in ℝ 3 \ s where Φ denotes the perturbation velocity potential, induced by the presence of the wings and s := L U W with the projection L of the wings onto the ( x,y)‐ plane and the wake W. Not all Cauchy data are given explicitly on L , respectively W . These missing Cauchy data depend on the wing circulation Γ· Γ has to be fixed by the Kutta–Joukovskii condition: Λ Φ should be finite near the trailing edge x t of L . To fulfil this condition in a way that all appearing terms can be defined mathematically exactly and belong to spaces which are physically meaningful, we propose to fix Γ by the condition of vanishing stress intensity factors of Φ near x t up to a certain order such that ΛΦ| xt ϵ W 2 ϵ ( x t )⊂ L 2 ( x t ),ϵ>0. In the two–dimensional case, and if L is the left half–plane in ℝ 2 , we have an explicit formula to calculate Γ and we can control the regularity of Γ and Φ.