3 citations · 13 across the 15 of their papers we have counts for
15 papers
Uniqueness and stability of steady vortex rings for 3D incompressible Euler equation
Daomin Cao, Shanfa Lai, Guolin Qin +2
In this paper, we are concerned with the uniqueness and nonlinear stability of vortex rings for the 3D Euler equation. By utilizing Arnold 's variational principle for steady state…
Existence, uniqueness and stability of steady vortex rings of small cross-section
Daomin Cao, Guolin Qin, Weilin Yu +2
This paper is concerned with steady vortex rings in an ideal fluid of uniform density, which are special global axi-symmetric solutions of the three-dimensional incompressible Eule…
On the existence of vortex-wave systems to inviscid gSQG equation
Daomin Cao, Shanfa Lai, Changjun Zou
We study the existence of different vortex-wave systems for inviscid gSQG flow, where the total circulation are produced by point vortices and vortices with compact support. To ove…
Co-rotating and traveling vortex sheets for the 2D incompressible Euler equation
Daomin Cao, Guolin Qin, Changjun Zou
We construct co-rotating and traveling vortex sheets for 2D incompressible Euler equation, which are supported on several small closed curves. These examples represent a new type o…
Existence of stationary vortex sheets for the 2D Euler equation
Daomin Cao, Guolin Qin, Changjun Zou
We investigate a steady planar flow of an ideal fluid in a (bounded or unbounded) domain . Let , , be arbitrary fixed constants…
Kármán vortex street for the generalized surface quasi-geostrophic equation
Daomin Cao, Guolin Qin, Weicheng Zhan +1
We are concerned with the existence of periodic travelling-wave solutions for the generalized surface quasi-geostrophic (gSQG) equation(including incompressible Euler equation), kn…
On the global classical solutions for the generalized SQG equation
Daomin Cao, Guolin Qin, Weicheng Zhan +1
In this paper, we study the existence of global classical solutions to the generalized surface quasi-geostrophic equation. By using the variational method, we provide some new fami…
Existence of co-rotating and travelling vortex patches with doubly connected components for active scalar equations
Daomin Cao, Guolin Qin, Weicheng Zhan +1
By applying implicit function theorem on contour dynamics, we prove the existence of co-rotating and travelling patch solutions for both Euler and the generalized surface quasi-geo…
Existence and stability of smooth traveling circular pairs for the generalized surface quasi-geostrophic equation
Daomin Cao, Guolin Qin, Weicheng Zhan +1
In this paper, we construct smooth travelling counter-rotating vortex pairs with circular supports for the generalized surface quasi-geostrophic equation. These vortex pairs are an…
Existence and regularity of co-rotating and travelling global solutions for the generalized SQG equation
Daomin Cao, Guolin Qin, Weicheng Zhan +1
By studying the linearization of contour dynamics equation and using implicit function theorem, we prove the existence of co-rotating and travelling global solutions for the gSQG e…
Global solutions for the generalized SQG equation and rearrangements
Daomin Cao, Guolin Qin, Weicheng Zhan +1
In this paper, we study the existence of rotating and traveling-wave solutions for the generalized surface quasi-geostrophic (gSQG) equation. The solutions are obtained by maximiza…
Multi-soliton dynamics in the nonlinear Schrödinger equation
Daomin Cao, Qing Guo, Changjun Zou
In this paper, we study the Cauchy problem of the nonlinear Schrödinger equation with a nontrival potential . In particular, we consider the case where the initia…
Local uniqueness of vortices for 2D steady Euler flow in a bounded domain
Daomin Cao, Weilin Yu, Changjun Zou
We study the 2D Euler equation in a bounded simply-connected domain, and establish the local uniqueness of flow whose stream function satisfies \begin{equation*} \b…
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…
On desingularization of steady vortex in the lake equations
Daomin Cao, Weicheng Zhan, Changjun Zou
We constructed a family of steady vortex solutions for the lake equations with general vorticity function, which constitute a desingularization of a singular vortex. The precise lo…