8 papers
An improved bound on the support diameter of nonnegative planar Euler vorticity
Daomin Cao, Junhong Fan, Guodong Wang
We prove an bound on the support radius of nonnegative planar Euler vorticity with compactly supported initial data, removing the logarithmic factors from the cl…
Gradient growth and relaxation to jump profiles for 3-fold symmetric scale-invariant Euler flows
Daomin Cao, Junhong Fan, Guolin Qin
We consider long-time behavior of the zero-homogeneous solutions with 3-fold symmetry to the two-dimensional Euler equation. This is the remaining case in the relaxation theory of…
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…
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|\…
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…
Expansion of Green's function and regularity of Robin's function for elliptic operators in divergence form
Daomin Cao, Jie Wan
We consider Green's function of the elliptic operator in divergence form on a bounded smooth domain $ Ω\subseteq\mathbb{R}^n (n\g…
Clustered helical vortices for 3D incompressible Euler equation in infinite cylinders
Daomin Cao, Jie Wan
In this article, we first consider solutions to a semilinear elliptic problem in divergence form \begin{equation*} \begin{cases} -\varepsilon^2\text{div}(K(x)\nabla u)= (u-q|\ln\va…