ABSTRACT

Let L be the curve delimiting an airfoil in potential incompressible flow whose velocity is

where i, j are orthogonal unit vectors on the axes OX, OY, respectively; M is a point on the plane OXY; Φ0(M) is a harmonic function defined on the entire plane. We assume that the curve L admits a parametric representation x=x(t), y=y(t), where is the arc length. The curve L is oriented clockwise, if L is closed. The functions x′(t) and y'(t) are supposed to satisfy the Hölder condition on [0, l] with exponent α, i.e., on [0, l]. Since t is the arc length, we have x′2(t)+y′2(t)≡1 for . If L is a closed curve, the functions x(t), y(t) and their derivatives are periodic with period l, which is assumed equal to 2π for simplicity.