4 papers · 1 filter
Symmetry in Serrin-type overdetermined problems
Daomin Cao, Juncheng Wei, Weicheng Zhan
This paper investigates the geometric constraints imposed on a domain by overdetermined problems for partial differential equations. Serrin's symmetry results are extended to overd…
Helical kelvin waves for the 3D Euler equation
Daomin Cao, Boquan Fan, Rui Li +1
Helical Kelvin waves were conjectured to exist for the 3D Euler equations in Lucas and Dritschel \cite{LucDri} (as well as in \cite{Chu}) by studying dispersion relation for infini…
Free boundary problems for the two-dimensional Euler equations in exterior domains
Daomin Cao, Boquan Fan, Weicheng Zhan
In this paper we present some classification results for the steady Euler equations in two-dimensional exterior domains with free boundaries. We prove that, in an exterior domain,…
Symmetry of uniformly rotating solutions for the vortex-wave system
Daomin Cao, Boquan Fan, Rui Li
In this paper, we study the radial symmetry properties of stationary and uniformly rotating solutions of the vortex-wave system introduced by Marchioro and Pulvirenti \cite{Mar1}.…