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UID:news473@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20181228T200306
DTSTART;TZID=Europe/Zurich:20141105T161500
SUMMARY:Seminar Analysis: Sara Daneri (Max Planck Institute for Mathematics
  in the Sciences\, Leipzig)
DESCRIPTION:We consider the Cauchy problem for the incompressible Euler equ
 ations on the three-dimensional torus. According to a conjecture due to On
 sager\, which is well known in turbulence theory\, while all the solutions
  which are uniformly α-Hölder continuous in space for any α>1/3 must co
 nserve the total kinetic energy\, for any α<1/3 there can be uniformly α
 -Hölder solutions which are strictly dissipative. While the first part of
  the conjecture is well established since a long time\, the second part is
  still open in its full generality. In the result that we present we show 
 that\, for any α<1/5\, there exist Cα vector fields being the initial da
 ta of infinitely many Cα solutions of the Euler equations which dissipate
  the total kinetic energy.
X-ALT-DESC: \nWe consider the Cauchy problem for the incompressible Euler e
 quations on the three-dimensional torus. According to a conjecture due to 
 Onsager\, which is well known in turbulence theory\, while all the solutio
 ns which are uniformly α-Hölder continuous in space for any α&gt\;1/3 m
 ust conserve the total kinetic energy\, for any α&lt\;1/3 there can be un
 iformly α-Hölder solutions which are strictly dissipative. While the fir
 st part of the conjecture is well established since a long time\, the seco
 nd part is still open in its full generality. In the result that we presen
 t we show that\, for any α&lt\;1/5\, there exist C<sup>α</sup> vector fi
 elds being the initial data of infinitely many C<sup>α</sup> solutions of
  the Euler equations which dissipate the total kinetic energy.
DTEND;TZID=Europe/Zurich:20141105T171500
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