4 papers
Piecewise smooth stationary Euler flows with support in a neighborhood of a helix
Daniel Peralta-Salas, Jie Wan
We construct stationary solutions of the three-dimensional incompressible Euler equations with helical symmetry and support in a neighborhood of a helix. The solutions are piecewis…
Co-rotating nearly parallel helical vortices with small cross-section in 3D incompressible Euler equations
Daomin Cao, Jie Wan
In this article, we consider clustered solutions to a semilinear elliptic equation in divergence form \begin{equation*} \begin{cases} -\varepsilon^2\text{div}(K(x)\nabla u)= (u-q|\…
Dynamics and leapfrogging phenomena of multiple helical vortices for 3D incompressible Euler equations
Daomin Cao, Junhong Fan, Guolin Qin +1
In this paper, we investigate the time evolution of helical vortices without swirl for the incompressible Euler equations in under general initial assumptions. Assume…
On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl
Guolin Qin, Jie Wan
In this paper, we consider the existence of concentrated helical vortices of 3D incompressible Euler equations with swirl. First, without the assumption of the orthogonality condit…