12 citations · 39 across the 26 of their papers we have counts for
26 papers
Global persistence of nearly radial concentrated vortices in a bounded domain
Daomin Cao, Guodong Wang
In this paper, we study the evolution of nearly radial concentrated vortices for the incompressible Euler equation in a bounded planar domain. We prove that if a single vortex is i…
Stability of degree-2 Rossby-Haurwitz waves
Daomin Cao, Guodong Wang, Bijun Zuo
Rossby-Haurwitz (RH) waves are important explicit solutions of the incompressible Euler equation on a two-dimensional rotating sphere. In this paper, we prove the orbital stability…
Stable plane Euler flows with concentrated and sign-changing vorticity
Guodong Wang, Bijun Zuo
We construct a family of steady solutions to the two-dimensional incompressible Euler equation in a general bounded domain, such that the vorticity is supported in two well-separat…
Nonlinear stability of sinusoidal Euler flows on a flat two-torus
Guodong Wang, Bijun Zuo
Sinusoidal flows are an important class of explicit stationary solutions of the two-dimensional incompressible Euler equations on a flat torus. For such flows, the steam functions…
An extension of Arnold's second stability theorem in a multiply-connected domain
Guodong Wang, Bijun Zuo
We give a sufficient condition for the nonlinear stability of steady flows of a two-dimensional ideal fluid in a bounded multiply-connected domain, which generalizes a stability cr…
On concentrated traveling vortex pairs with prescribed impulse
Guodong Wang
In this paper, we consider a constrained maximization problem related to planar vortex pairs with prescribed impulse. We prove existence, stability and asymptotic behavior for the…
Asymptotic estimates for concentrated vortex pairs
Guodong Wang
In [Comm. Math. Phys. 324 (2013), 445--463], Burton-Lopes Filho-Nussenzveig Lopes studied the existence and stability of slowly traveling vortex pairs as maximizers of the kinetic…
Stability of two-dimensional steady Euler flows with concentrated vorticity
Guodong Wang
In this paper, we study the stability two-dimensional (2D) steady Euler flows with sharply concentrated vorticity in a simply-connected bounded domain. These flows are obtained as…
Nonlinear stability of planar steady Euler flows associated with semistable solutions of elliptic problems
Guodong Wang
This paper is devoted to the study of nonlinear stability of steady incompressible Euler flows in two dimensions. We prove that a steady Euler flow is nonlinearly stable in n…
Stability of 2D steady Euler flows related to least energy solutions of the Lane-Emden equation
Guodong Wang
In this paper, we investigate nonlinear stability of planar steady Euler flows related to least energy solutions of the Lane-Emden equation in a smooth bounded domain. We prove the…
Global existence of weak solutions to the compressible Navier-Stokes equations with temperature-depending viscosity coefficients
Guodong Wang, Bijun Zuo
This paper is devoted to the global existence of weak solutions to the three-dimensional compressible Navier-Stokes equations with heat-conducting effects in a bounded domain. The…
Location of concentrated vortices in planar steady Euler flows
Guodong Wang, Bijun Zuo
In this paper, we study two-dimensional steady incompressible Euler flows in which the vorticity is sharply concentrated in a finite number of regions of small diameter in a bounde…
Singularity for a multidimensional variational wave equation arising from nematic liquid crystals
Yanbo Hu, Guodong Wang
This article is focused on a multidimensional nonlinear variational wave equation which is the Euler-Lagrange equation of a variational principle arising form the theory of nematic…
Steady vortex flows of perturbation type in a planar bounded domain
Daomin Cao, Guodong Wang, Zhan Weicheng
In this paper, we investigate steady Euler flows in a two-dimensional bounded domain. By an adaption of the vorticity method, we prove that for any nonconstant harmonic function $q…
Desingularization of vortices for 2D steady Euler flows via the vorticity method
Daomin Cao, Guodong Wang, Weicheng Zhan
In this paper, we consider steady Euler flows in a planar bounded domain in which the vorticity is sharply concentrated in a finite number of disjoint regions of small diameter. Su…
On radial symmetry of rotating vortex patches in the disc
Guodong Wang, Bijun Zuo
In this note, we consider the radial symmetry property of rotating vortex patches for the 2D incompressible Euler equations in the unit disc. By choosing a suitable vector field to…
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…
Steady vortex patches near a rotating flow with constant vorticity in a planar bounded domain
Guodong Wang, Bijun Zuo
In this paper, we study steady vortex patch solutions to the incompressible Euler equations in a planar bounded domain . Let be the solution of the elliptic problem $-Δψ_{…
Steady vortex patches near a nontrivial irrotational flow
Daomin Cao, Guodong Wang, Weicheng Zhan
In this paper, we study the vortex patch problem in an ideal fluid in a planar bounded domain. By solving a certain minimization problem and studying the limiting behavior of the m…
Existence of steady symmetric vortex patch in a disk
Daomin Cao, Guodong Wang, Bijun Zuo
In this paper we construct a family of steady symmetric vortex patches for the incompressible Euler equations in an open disk. The result is obtained by studying a variational prob…
Existence of steady multiple vortex patches to the vortex-wave system
Daomin Cao, Guodong Wang
In this paper we prove the existence of steady multiple vortex patch solutions to the vortex-wave system in a planar bounded domain. The construction is performed by solving a cert…
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…
Steady vortex patch solutions to the vortex-wave system
Daomin Cao, Guodong Wang
The vortex-wave system describes the motion of a two-dimensional ideal fluid in which the vorticity includes continuously distributed vorticity, which is called the background vort…
Euler evolution of a concentrated vortex in planar bounded domains
Daomin Cao, Guodong Wang
In this paper, we consider the time evolution of an ideal fluid in a planar bounded domain. We prove that if the initial vorticity is supported in a sufficiently small region with…