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SUMMARY:Uniqueness of the Leray-Hopf solution for a dyadic model - Filonov
 \, N (Russian Academy of Sciences St Peterburg)
DTSTART:20150603T141000Z
DTEND:20150603T151000Z
UID:TALK59663@talks.cam.ac.uk
CONTACT:42080
DESCRIPTION:We consider the system of nonlinear differential equations\n\n
 \nlabel{1}\negin{cases}\ndot u_n(t) + la^{2n} u_n(t) \n- la^{e n} u_{n-1
 }(t)^2 + la^{e(n+1)} u_n(t) u_{n+1}(t) = 0\,\\\nu_n(0) = a_n\, n in mathb
 b{N}\, quad la > 1\, e > 0.\n\nIn this talk we explain why this system is
  a model for the Navier-Stokes equations of hydrodynamics. The natural que
 stion is to find a such functional space\, where one could prove the exist
 ence and the uniqueness of solution. In 2008\, A.~Cheskidov proved that th
 e system (0.1) has a unique "strong" solution if $e le 2$\, whereas the "
 strong" solution does not exist if $e > 3$.\n\n(Note\, that the 3D-Navier
 -Stokes equations correspond to the value $e = 5/2$.)\n\nWe show that for
  sufficiently "good" initial data the system (0.1)has a unique Leray-Hopf 
 solution for all $e > 0$.\n\n
LOCATION:Seminar Room 2\, Newton Institute Gatehouse
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