Planar limits of three-dimensional incompressible flows with helical symmetry (Q487939)

The authors study the planar limits of three-dimensional incompressible Navier-Stokes equations and Euler equations with helical symmetry with no-slip and no-penetration boundary conditions respectively in an infinite circular pipe. As the key parameter in helical symmetry tends to infinity, the authors show the limit of three-dimensional helical Navier-Stokes equations and Euler equations satisfies the so-called two and half Navier-Stokes equations and Euler equations, respectively.