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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Uniqueness of the Leray-Hopf solution for a dyadic model

## Uniqueness of the Leray-Hopf solution for a dyadic modelAdd to your list(s) Download to your calendar using vCal - Filonov, N (Russian Academy of Sciences St Peterburg)
- Wednesday 03 June 2015, 15:10-16:10
- Seminar Room 2, Newton Institute Gatehouse.
If you have a question about this talk, please contact webseminars. Periodic and Ergodic Spectral Problems We consider the system of nonlinear differential equations label{1}
egin{cases}
dot u_n(t) + la In this talk we explain why this system is a model for the Navier-Stokes equations of hydrodynamics. The natural question is to find a such functional space, where one could prove the existence and the uniqueness of solution. In 2008, A.~Cheskidov proved that the system (0.1) has a unique “strong” solution if $e le 2$, whereas the “strong” solution does not exist if $e > 3$. (Note, that the 3D-Navier-Stokes equations correspond to the value $e = 5/2$.) We show that for sufficiently “good” initial data the system (0.1)has a unique Leray-Hopf solution for all $e > 0$. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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