Ort: Spiegelgasse 1, Seminarraum 00.003
Lamb dipole is an explicit traveling wave solution of the two-dimensional incompressible Euler equations, described by Lamb back in 1895. Due to difficulties arising from the fact that it is the dipole with "maximal mass" under enstrophy and impulse constraints, its nonlinear orbital stability was proved only in 2022 by Abe and Choi. Our main result is the nonlinear orbital stability of linear superpositions of Lamb dipoles, allowing for dipoles with mixed signs. Such a configuration is not a local extremizer of the kinetic energy, which is the main challenge in applying the variational principle to obtain stability. Furthermore, when dipoles have mixed signs, the impulse is not coercive anymore. These issues are handled by Lagrangian bootstrapping schemes, which carefully track the space-time location of various parts of the solution. This is based on joint works with Ken Abe, Kyudong Choi, Guolin Qin, and Yao Yao.
Veranstaltung übernehmen als iCal