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SUMMARY:An Explicit Filtered Lie Splitting Scheme for the Original Zakharo
 v System with Low Regularity Error Estimates in All Dimensions - Hang Li (
 Sorbonne Université)
DTSTART:20250501T140000Z
DTEND:20250501T150000Z
UID:TALK225679@talks.cam.ac.uk
CONTACT:Georg Maierhofer
DESCRIPTION:In this talk\, we present low-regularity numerical schemes for
  nonlinear dispersive equations\, with a particular focus on the Zakharov 
 system (ZS) and the “good” Boussinesq (GB) equation. These models exhi
 bit strong nonlinear interactions and are known to pose significant analyt
 ical and numerical challenges when the solution has limited regularity.\n\
 nWe concentrate on our recent results for the Zakharov system\, where we c
 onstruct and analyze an explicit filtered Lie splitting scheme applied dir
 ectly to its original coupled form. This method successfully overcomes the
  essential difficulty of derivative loss in the nonlinear terms\, which no
 t only obstructs low-regularity analysis\, but has long prevented rigorous
  error estimates for explicit Lie splitting schemes based directly on the 
 original Zakharov system. By developing multilinear estimates in discrete 
 Bourgain spaces\, we rigorously prove the first explicit low-regularity er
 ror estimate for the original Zakharov system\, and also the first such re
 sult for a coupled system within the Bourgain framework. The analytical st
 rategy developed here can also be extended to other dispersive equations w
 ith derivative loss\, offering a way to overcome both low-regularity di
 fficulties and the fundamental obstacle posed by derivative-loss nonlinear
 ities. Numerical experiments confirm the theoretical predictions.
LOCATION:Centre for Mathematical Sciences\, MR14
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