  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 Euler flows with helical symmetry, 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. By using the stream-function method, we
show the existence and asymptotic behavior of ground state solutions
concentrating near a single point as the parameter $ \varepsilon\to 0 $.
Qualitative properties of those solutions are also discussed.

Analysis of PDEs