Steady vortex rings with swirl in an ideal fluid: asymptotics for some solutions in exterior domains. (Q1775154)

The paper deals with the axisymmetric flow of an ideal fluid outside the cylinder. Rewriting the generalized equations in cylindrical coordinates and supposing that \(\theta \)-component of the velocity is not constant (it means steady vortex rings with swirl) the asymptotic behavior is investigated. The author shows that if \(k\) (flux constant) tends to \(\infty \) that (i)\ \(dist (0z,\partial A)=0(k^{1/});diam ~A =0(exp(-c_0 k^{3/2}));\) (ii)\ \((k^{1/2}\psi )_{k\in N}\) converges to a vortex cylinder \(U_m\) if \(m\leq q+2\) and if \(m>q+2\) it converges to \(U_{q+2}\).