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UID:news2059@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20260623T165730
DTSTART;TZID=Europe/Zurich:20260702T164500
SUMMARY:Another Afternoon of Fluid Dynamics: In-Jee Jeong (Korea Institute 
 for Advanced Study)
DESCRIPTION:Lamb dipole is an explicit traveling wave solution of the two-d
 imensional incompressible Euler equations\, described by Lamb back in 1895
 . Due to difficulties arising from the fact that it is the dipole with "ma
 ximal mass" under enstrophy and impulse constraints\, its nonlinear orbita
 l stability was proved only in 2022 by Abe and Choi. Our main result is th
 e nonlinear orbital stability of linear superpositions of Lamb dipoles\, a
 llowing 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 sp
 ace-time location of various parts of the solution. This is based on joint
  works with Ken Abe\, Kyudong Choi\, Guolin Qin\, and Yao Yao. 
X-ALT-DESC:<p>Lamb dipole is an explicit traveling wave solution of the two
 -dimensional incompressible Euler equations\, described by Lamb back in 18
 95. Due to difficulties arising from the fact that it is the dipole with "
 maximal mass" under enstrophy and impulse constraints\, its nonlinear orbi
 tal 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 loca
 l extremizer of the kinetic energy\, which is the main challenge in applyi
 ng the variational principle to obtain stability. Furthermore\, when dipol
 es have mixed signs\, the impulse is not coercive anymore. These issues ar
 e handled by Lagrangian bootstrapping schemes\, which carefully track the 
 space-time location of various parts of the solution. This is based on joi
 nt works with Ken Abe\, Kyudong Choi\, Guolin Qin\, and Yao Yao.&nbsp\;</p
 >
DTEND;TZID=Europe/Zurich:20260702T174500
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