A Note on the Regularity Criterion of Weak Solutions of Navier-Stokes Equations in Lorentz Space

Xunwu Yin

Abstract and Applied Analysis, 2012, vol. 2012, 1-9

Abstract:

This paper is concerned with the regularity of Leray weak solutions to the 3D Navier-Stokes equations in Lorentz space. It is proved that the weak solution is regular if the horizontal velocity denoted by ̃ ð ‘¢ = ( ð ‘¢ 1 , ð ‘¢ 2 , 0 ) satisfies ̃ ð ‘¢ ( ð ‘¥ , ð ‘¡ ) ∈ ð ¿ ð ‘ž ( 0 , 𠑇 ; ð ¿ ð ‘ , ∞ ( ð ‘ 3 ) ) f o r 2 / ð ‘ž + 3 / ð ‘ = 1 , 3 < ð ‘ < ∞ . The result is obvious and improved that of Dong and Chen (2008) on the Lebesgue space.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:184674

DOI: 10.1155/2012/184674

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