Desingularization of 3D steady Euler equations with helical symmetry

In this paper, we study desingularization of steady solutions of 3D incompressible Euler equation with helical symmetry in a general helical domain. We construct a family of steady helical Euler flows, such that the associated vorticities tend asymptotically to a helical vortex filament. The solutions are obtained by solving a semilinear elliptic problem in divergence form with a parameter-epsilon(2)div(K-H(x)del u) = f (u - q| ln epsilon|) in 0, u = 0 on partial derivative 52.By using the variational method, we show that for any 0 < epsilon < 1, there exist ground states concentrating near minimum points of q(2)root det(K-H) as the parameter epsilon -> 0. These results show a striking difference with the 2D and the 3D axisymmetric Euler equation cases.