Mathematics – General Mathematics
Scientific paper
2008-09-21
Electronic Journal of Differential Electron. Journal of Diff. Equ. 2010(2010), No 93, pp. 1-14
Mathematics
General Mathematics
This is the version of the paper published in the peer-reviewed journal. Notice, this paper received 25 months of review in fo
Scientific paper
The paper proves Statement D in the Navier-Stokes problem posed by the Clay Mathematics Institute. The paper has been published in a peer-reviewed journal. The proof proceeds as follows. The Clay Math Institute's problem formulation does not require the pressure to be space-periodic. There are several solutions that are not space-periodic to zero external force. The Clay Math Institute's problem formulation does not state that the external force cannot be a feedback control force, and indeed it must be in this case if the problem formulation is expected to be without errors. A feedback control force can select a solution which has a finite time blow-up. Thus, we have space periodic initioal conditions, space periodic external force satisfying required conditions and a smooth periodic solution for u(x,t) which has a finite time blow-up. Recovering the "original" problem requires several chnges and is not done by a minor modification. Simple, yes very, but was not that easy to invent and had it been so easy, why was it not invented before?
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