5 papers
Gradient growth and relaxation to jump profiles for 3-fold symmetric scale-invariant Euler flows
Daomin Cao, Junhong Fan, Guolin Qin
We consider the zero-homogeneous reduction of the two-dimensional Euler equation in the 3-fold symmetric case , which is left unsolved in the relaxation theory of Sai…
Growth of vorticity gradient for the Euler equation on the sphere
Daomin Cao, Junhong Fan, Guolin Qin
We prove that for solutions of the Euler equation on the sphere, the vorticity gradient can grow at most double-exponentially in time, and we show that this upper bound is sharp by…
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…
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…