A Note on the Regularity Criterion of Weak Solutions of Navier-Stokes Equations in Lorentz Space
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 ũ=(u1,u2,0) satisfies ũ(x,t)∈Lq(0,T;Lp,∞(R3)) for 2/q + 3/p=1, 3<p<∞. The result is...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/184674 |
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| _version_ | 1832567203286745088 |
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| author | Xunwu Yin |
| author_facet | Xunwu Yin |
| author_sort | Xunwu Yin |
| collection | DOAJ |
| description | 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 ũ=(u1,u2,0) satisfies ũ(x,t)∈Lq(0,T;Lp,∞(R3)) for 2/q + 3/p=1, 3<p<∞. The result is obvious and improved that of Dong and Chen (2008) on the Lebesgue space. |
| format | Article |
| id | doaj-art-dc4ad51eef2d41d299fddb779784df9e |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-dc4ad51eef2d41d299fddb779784df9e2025-02-03T01:02:15ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/184674184674A Note on the Regularity Criterion of Weak Solutions of Navier-Stokes Equations in Lorentz SpaceXunwu Yin0School of Science, Tianjin Polytechnic University, Tianjin 300387, ChinaThis 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 ũ=(u1,u2,0) satisfies ũ(x,t)∈Lq(0,T;Lp,∞(R3)) for 2/q + 3/p=1, 3<p<∞. The result is obvious and improved that of Dong and Chen (2008) on the Lebesgue space.http://dx.doi.org/10.1155/2012/184674 |
| spellingShingle | Xunwu Yin A Note on the Regularity Criterion of Weak Solutions of Navier-Stokes Equations in Lorentz Space Abstract and Applied Analysis |
| title | A Note on the Regularity Criterion of Weak Solutions of Navier-Stokes Equations in Lorentz Space |
| title_full | A Note on the Regularity Criterion of Weak Solutions of Navier-Stokes Equations in Lorentz Space |
| title_fullStr | A Note on the Regularity Criterion of Weak Solutions of Navier-Stokes Equations in Lorentz Space |
| title_full_unstemmed | A Note on the Regularity Criterion of Weak Solutions of Navier-Stokes Equations in Lorentz Space |
| title_short | A Note on the Regularity Criterion of Weak Solutions of Navier-Stokes Equations in Lorentz Space |
| title_sort | note on the regularity criterion of weak solutions of navier stokes equations in lorentz space |
| url | http://dx.doi.org/10.1155/2012/184674 |
| work_keys_str_mv | AT xunwuyin anoteontheregularitycriterionofweaksolutionsofnavierstokesequationsinlorentzspace AT xunwuyin noteontheregularitycriterionofweaksolutionsofnavierstokesequationsinlorentzspace |