4 citations · 10 across the 14 of their papers we have counts for
14 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…
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…
Structure of Green's function of elliptic equations and helical vortex patches for 3D incompressible Euler equations
Daomin Cao, Jie Wan
We develop a new structure of the Green's function of a second-order elliptic operator in divergence form in a 2D bounded domain. Based on this structure and the theory of rearrang…
Helical vortices with small cross-section for 3D incompressible Euler equation
Daomin Cao, Jie Wan
In this article, we construct traveling-rotating helical vortices with small cross-section to the 3D incompressible Euler equations in an infinite pipe, which tend asymptotically t…
Desingularization of 3D steady Euler equation with helical symmetry
Daomin Cao, Jie Wan
In this paper, we study desingularization of steady solutions of 3D incompressible Euler equation with helical symmetry in a general helical domain. We construct a family of steady…
Desingularization of steady vortex of perturbation type in the lake equations
Daomin Cao, Jie Wan, Changjun Zou
In this paper, we study the desingularization of steady lake model of perturbation type with general nonlinearity f. Using the modified vorticity method, we construct a family of s…
Desingularization of vortex rings in 3 dimensional Euler flows: with swirl
Daomin Cao, Jie Wan, Weicheng Zhan
We study desingularization of steady vortex rings in three-dimensional axisymmetric incompressible Euler fluids with swirl. Using the variational method, we construct a two-paramet…
Rotating vortex patches for the planar Euler equations in a disk
Daomin Cao, Jie Wan, Guodong Wang +1
We construct a family of rotating vortex patches with fixed angular velocity for the two-dimensional Euler equations in a disk. As the vorticity strength goes to infinity, the limi…
Desingularization of vortex rings in 3 dimensional Euler flows
Daomin Cao, Jie Wan, Weicheng Zhan
In this paper, we are concerned with nonlinear desingularization of steady vortex rings of three-dimensional incompressible Euler fluids. We focus on the case when the vorticity fu…
Nonlinear Orbital Stability for Planar Vortex Patches
Daomin Cao, Guodong Wang, Jie Wan
In this paper, we prove nonlinear orbital stability for steady vortex patches that maximize the kinetic energy among isovortical rearrangements in a planar bounded domain. As a res…