An estimate for the vorticity of the Navier-Stokes equation
Let over(u, →) (ṡ, t) be a strong solution of the Navier-Stokes equation on 3-dimensional torus T3, and over(ω, →) (ṡ, t) = ∇ × over(u, →) (ṡ, t) be the vorticity. In this Note we show that{norm of matrix} over(ω, →) (ṡ, t) {norm of matrix}1 + frac(sqrt(2), 4 ν) {norm of matrix} over(u, →) (ṡ, t) {n...
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| Format: | Journal article |
| Language: | English |
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2009
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| _version_ | 1797079972523802624 |
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| author | Qian, Z |
| author_facet | Qian, Z |
| author_sort | Qian, Z |
| collection | OXFORD |
| description | Let over(u, →) (ṡ, t) be a strong solution of the Navier-Stokes equation on 3-dimensional torus T3, and over(ω, →) (ṡ, t) = ∇ × over(u, →) (ṡ, t) be the vorticity. In this Note we show that{norm of matrix} over(ω, →) (ṡ, t) {norm of matrix}1 + frac(sqrt(2), 4 ν) {norm of matrix} over(u, →) (ṡ, t) {norm of matrix}22 is decreasing in t as long as the solution over(u, →) (ṡ, t) exists, where ν > 0 is the viscosity constant and {norm of matrix} ṡ {norm of matrix}q denotes the Lq-norm. To cite this article: Z. Qian, C. R. Acad. Sci. Paris, Ser. I 347 (2009). © 2008 Académie des sciences. |
| first_indexed | 2024-03-07T00:53:32Z |
| format | Journal article |
| id | oxford-uuid:87370fd1-5f7f-467c-a3a1-8fc70b23c105 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T00:53:32Z |
| publishDate | 2009 |
| record_format | dspace |
| spelling | oxford-uuid:87370fd1-5f7f-467c-a3a1-8fc70b23c1052022-03-26T22:09:18ZAn estimate for the vorticity of the Navier-Stokes equationJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:87370fd1-5f7f-467c-a3a1-8fc70b23c105EnglishSymplectic Elements at Oxford2009Qian, ZLet over(u, →) (ṡ, t) be a strong solution of the Navier-Stokes equation on 3-dimensional torus T3, and over(ω, →) (ṡ, t) = ∇ × over(u, →) (ṡ, t) be the vorticity. In this Note we show that{norm of matrix} over(ω, →) (ṡ, t) {norm of matrix}1 + frac(sqrt(2), 4 ν) {norm of matrix} over(u, →) (ṡ, t) {norm of matrix}22 is decreasing in t as long as the solution over(u, →) (ṡ, t) exists, where ν > 0 is the viscosity constant and {norm of matrix} ṡ {norm of matrix}q denotes the Lq-norm. To cite this article: Z. Qian, C. R. Acad. Sci. Paris, Ser. I 347 (2009). © 2008 Académie des sciences. |
| spellingShingle | Qian, Z An estimate for the vorticity of the Navier-Stokes equation |
| title | An estimate for the vorticity of the Navier-Stokes equation |
| title_full | An estimate for the vorticity of the Navier-Stokes equation |
| title_fullStr | An estimate for the vorticity of the Navier-Stokes equation |
| title_full_unstemmed | An estimate for the vorticity of the Navier-Stokes equation |
| title_short | An estimate for the vorticity of the Navier-Stokes equation |
| title_sort | estimate for the vorticity of the navier stokes equation |
| work_keys_str_mv | AT qianz anestimateforthevorticityofthenavierstokesequation AT qianz estimateforthevorticityofthenavierstokesequation |