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On the blow‐up criterion of the periodic incompressible fluids
Journal article   Peer reviewed

On the blow‐up criterion of the periodic incompressible fluids

Jamel Benameur
Mathematical methods in the applied sciences, Vol.36(2), pp.143-153
30/01/2013
DOI: https://doi.org/10.1002/mma.2577

Abstract

blow‐up criterion Euler equations Navier–Stokes equations periodic incompressible fluids Sobolev spaces
Kato, Ponce, Beale and Majda prove the existence and uniqueness of maximal solution of Euler and Navier–Stokes equations and some blow‐up criterion. In the periodic case, we establish that if the maximum time T* is finite, then the growth of ∥u(t)∥Hm is at least of the order of (T* − t)−2m / 5. Copyright © 2012 John Wiley & Sons, Ltd.

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