题目：Stability of vortex quadrupoles with odd-odd symmetry

报告人: In-Jee Jeong (首尔国立大学，韩国)

时间: 1月21日上午10:30-11:30

地点：五教5306

摘要：We establish global in time stability of vortex quadrupoles satisfying odd symmetry with respect to both axes, for 2D incompressible and inviscid flows. Specifically, if the vorticity restricted to a quadrant is signed, sufficiently concentrated and $L^{1}$ close to its radial rearrangement up to a translation, we prove that it remains so for all times. As a consequence of this stability, we obtain global desingularization results for a single point vortex defined in a quadrant. The main difficulty is that the kinetic energy maximization problem in a quadrant, which is the usual setup for establishing vortex stability, does not have a solution as the kinetic energy increases when vorticity escapes to infinity. We overcome this by taking dynamical information into account: finite-time desingularization result is combined with monotonicity of the first moment and a careful analysis of the interaction energies between vortices. The latter is achieved by new pointwise estimates on the Biot--Savart kernel and quantitative stability results for general interaction kernels. In addition, we obtain stability of a pair of opposite-signed Lamb dipoles moving away from each other. This is joint work with Kyudong Choi (UNIST) and Yao Yao (NUS).