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UID:250fe5922b6c6ad9090ffe9e0bc41ac6
CATEGORIES:Joint Princeton-Rutgers Seminar on Analysis of Fluids
CREATED:20260128T074414
SUMMARY:Elia Brue: Flexibility of two-dimensional Euler flows
LOCATION:Hill 705
DESCRIPTION:<p>Abstract: &nbsp;&nbsp;</p><p style="margin: 0px; font-style: normal; fon
 t-weight: normal; font-size: 11px; line-height: normal; font-family: Menlo;
  color: #000000;">We consider weak solutions of the two-dimensional Euler e
 quations with vorticity in L^p. Since Yudovich's work in 1962, it has been 
 known that the associated Cauchy problem is well posed when p = infinity. A
  classical open question is whether uniqueness still holds for finite p. We
  show that, for p &gt; 1 sufficiently close to 1, the problem is in fact co
 mpletely flexible in the sense of</p><p style="margin: 0px; font-style: nor
 mal; font-weight: normal; font-size: 11px; line-height: normal; font-family
 : Menlo; color: #000000;">Gromov's&nbsp; h-principle. In particular, we con
 struct weak solutions exhibiting a range of non-physical behaviors. As a co
 nsequence, this gives a negative answer to the uniqueness question for p &g
 t; 1 close to 1.</p>
CONTACT:Institute for Advanced Study and Bocconi University
DTSTAMP:20260827T015800
DTSTART;TZID=America/New_York:20260331T134000
DTEND;TZID=America/New_York:20260331T144000
SEQUENCE:0
TRANSP:OPAQUE
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