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Regularity criteria for the Navier–Stokes equations involving the ratio pressure-gradient of velocity

✍ Scribed by Manuel Núñez

Publisher
John Wiley and Sons
Year
2009
Tongue
English
Weight
142 KB
Volume
33
Category
Article
ISSN
0170-4214

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✦ Synopsis

A number of bounds upon the pressure are known to guarantee regularity of the solutions of the Navier-Stokes equations. Since the pressure is the potential whose source is the product of the velocity and its gradient, it is worth to consider bounds depending on the quotient of the pressure and some quantity measuring the size of this source. Estimates involving the ratio pressure-velocity are known. Our result includes the velocity gradient: if the ratio p 1+|v|+|∇v| r remains bounded for some r < 1, so does the velocity and therefore it retains its regularity.

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