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math.AP2025
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|\…
math.AP2025
Linear Growth of the Vorticity Maximum for Axisymmetric Euler Flows Without Swirl
Daomin Cao, Junhong Fan, Guolin Qin
We study long-time vortex stretching for three-dimensional axisymmetric Euler flows without swirl in the anti-parallel class associated with the head-on collision of two coaxial vo…
math.AP2025
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…