BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Quoc hung Nguyen (上海科技大学)
DTSTART:20201229T091500Z
DTEND:20201229T100000Z
DTSTAMP:20260423T024028Z
UID:iccm2020/88
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/iccm2020/88/
 ">The Muskat equation is well-posed on the critical Sobolev space</a>\nby 
 Quoc hung Nguyen (上海科技大学) as part of ICCM 2020\n\n\nAbstract\n
 This talk is about a series of papers with Thomas Alazard\, devoted to the
  study of solutions with critical regularity for the two-dimensional Muska
 t equation. I will describe our main result\, which states that the Cauchy
  problem is well-posed on the endpoint Sobolev space of L^2 functions with
  three-half derivative in L^2 (locally in time for large data\, and global
 ly for small enough data). This result is optimal with respect to the scal
 ing of the equation. For the proof\, we introduce weighted fractional lapl
 acians and use these operators to estimate the solutions for a norm which 
 depends on the initial data themselves. Another key ingredient of the proo
 f is a null-type structure\, allowing to compensate for the degeneracy of 
 the parabolic behavior for large slopes.\n
LOCATION:https://researchseminars.org/talk/iccm2020/88/
END:VEVENT
END:VCALENDAR