33 citations · 38 across the 3 of their papers we have counts for
3 papers
math.AP2020★ 2 cited
Compactness and stability for planar vortex-pairs with prescribed impulse
G. R. Burton
Concentration-compactness is used to prove compactness of maximising sequences for a variational problem governing symmetric steady vortex-pairs in a uniform planar ideal fluid flo…
math.AP2012★ 3 cited
On the stability of travelling waves with vorticity obtained by minimisation
B. Buffoni, G. R. Burton
We modify the approach of Burton and Toland [Comm. Pure Appl. Math. (2011)] to show the existence of periodic surface water waves with vorticity in order that it becomes suited to…
math.AP2012★ 33 cited
Nonlinear stabilitty for steady vortex pairs
Geoffrey R. Burton, Milton C. Lopes Filho, Helena J. Nussenzveig Lopes
In this article, we prove nonlinear orbital stability for steadily translating vortex pairs, a family of nonlinear waves that are exact solutions of the incompressible, two-dimensi…