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SUMMARY:Patrick Gérard (Université Paris-Saclay\, France)
DTSTART:20221103T163000Z
DTEND:20221103T173000Z
DTSTAMP:20260423T040035Z
UID:SIAM-PDE/25
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SIAM-PDE/25/
 ">A survey of the Benjamin-Ono equation with periodic boundary conditions<
 /a>\nby Patrick Gérard (Université Paris-Saclay\, France) as part of Sem
 inar In the Analysis and Methods of PDE (SIAM PDE)\n\n\nAbstract\nThe Benj
 amin-Ono equation is a nonlinear dispersive wave equation in one space dim
 ension\, introduced in 1967 as a model for long internal gravity waves in 
 a two layer fluid with infinite depth. In this talk\, I will show how the 
 use of a Lax pair provides a fairly complete picture of the dynamics with 
 periodic boundary conditions. I will discuss an explicit formula for the s
 olutions\, global well posedness in sharp regularity\,  long time dynamics
 \, the classification of traveling waves\, of multi-solitons  and of doubl
 y periodic solutions\, and the smoothing effect. This talk is inspired fro
 m a series of jointworks with Thomas Kappeler and Petar Topalov.\n
LOCATION:https://researchseminars.org/talk/SIAM-PDE/25/
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