TY - JOUR

T1 - Nonlinear stability of steady vortex pairs

AU - Burton, Geoffrey

AU - Nussenzveig Lopes, Helena

AU - Lopes Filho, Milton C.

PY - 2013/12

Y1 - 2013/12

N2 - 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-dimensional Euler equations. We use an adaptation of Kelvin's variational principle, maximizing kinetic energy penalised by a multiple of momentum among mirror-symmetric isovortical rearrangements. This formulation has the advantage that the functional to be maximized and the constraint set are both invariant under the flow of the time-dependent Euler equations, and this observation is used strongly in the analysis. Previous work on existence yields a wide class of examples to which our result applies.

AB - 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-dimensional Euler equations. We use an adaptation of Kelvin's variational principle, maximizing kinetic energy penalised by a multiple of momentum among mirror-symmetric isovortical rearrangements. This formulation has the advantage that the functional to be maximized and the constraint set are both invariant under the flow of the time-dependent Euler equations, and this observation is used strongly in the analysis. Previous work on existence yields a wide class of examples to which our result applies.

UR - http://www.scopus.com/inward/record.url?scp=84886900290&partnerID=8YFLogxK

UR - http://arxiv.org/abs/1206.5329

UR - http://dx.doi.org/10.1007/s00220-013-1806-y

U2 - 10.1007/s00220-013-1806-y

DO - 10.1007/s00220-013-1806-y

M3 - Article

SN - 0010-3616

VL - 324

SP - 445

EP - 463

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 2

ER -