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

Xiangou Zhu | Zendy

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

Author(s) -

Xiangou Zhu

Publication year - 2012

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2012/682436

Subject(s) - mathematics , multiplier (economics) , sobolev space , navier–stokes equations , mathematical analysis , class (philosophy) , pressure gradient , pure mathematics , compressibility , thermodynamics , mechanics , artificial intelligence , computer science , economics , macroeconomics , physics

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 L 2/(2 - r) ((0, T); (H r (ℝ 3) → H -r (ℝ3))), where (H r(ℝ 3) → H -r (ℝ 3)) is the multipliers between Sobolev spaces whose definition is given later for 0 < r < 1, then the Leray-Hopf weak solution to the Navier-Stokes equations is actually regular. Copyright © © 2012 Xiang'ou Zhu.

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