Polya Vector Field May 2026

[ \mathbfV_f = (u,, -v). ]

Thus (\nabla \psi = (v, u)). Check integrability: (\partial_x (v) = v_x = u_y) and (\partial_y (u) = u_y) — they match. So (\psi) exists (since domain simply connected). So: polya vector field

The of (f) is defined as the vector field in the plane given by [ \mathbfV_f = (u,, -v)