A note on necessary conditions for blow-up of energy solutions to the Navier-Stokes equations

Details A note on necessary conditions for blow-up of energy solutions to the Navier-Stokes equations A note on necessary conditions for blow-up of energy solutions to the Navier-Stokes equations

2009-09-22

arxiv.org/abs/0909.3897v1

Mathematics

Analysis of PDEs

Scientific paper

In the present note, we address the question about behavior of $L_3$-norm of
the velocity field as time $t$ approaches blow-up time $T$. It is known that
the upper limit of the above norm must be equal to infinity. We show that, for
blow-ups of type I, the lower limit of $L_3$-norm equals to infinity as well.

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