A Regularity Criterion for the Navier-Stokes Equations in the Multiplier Spaces

Xiang'ou Zhu

Abstract and Applied Analysis, 2012, vol. 2012, 1-7

Abstract:

We exhibit a regularity condition concerning the pressure gradient for the Navier-Stokes equations in a special class. It is shown that if the pressure gradient belongs to ð ¿ 2 / ( 2 − ð ‘Ÿ ) ̇ ð » ( ( 0 , 𠑇 ) ; ℳ ( ð ‘Ÿ ( â„ 3 ̇ ð » ) → − ð ‘Ÿ ( â„ 3 ) ) ) , where ̇ ð » â„³ ( ð ‘Ÿ ( â„ 3 ̇ ð » ) → − ð ‘Ÿ ( â„ 3 ) ) is the multipliers between Sobolev spaces whose definition is given later for 0 < ð ‘Ÿ < 1 , then the Leray-Hopf weak solution to the Navier-Stokes equations is actually regular.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:682436

DOI: 10.1155/2012/682436

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