Commentary on local and boundary regularity of weak solutions to Navier-Stokes equations
We present results on local and boundary regularity for weak solutions to the Navier-Stokes equations. Beginning with the regularity criterion proved recently in [14] for the Cauchy problem, we show that this criterion holds also locally. This is also the case for some other results: We present two...
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| Format: | Article |
| Language: | English |
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Texas State University
2004-01-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2004/09/abstr.html |
| _version_ | 1818389568196444160 |
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| author | Zdenek Skalak |
| author_facet | Zdenek Skalak |
| author_sort | Zdenek Skalak |
| collection | DOAJ |
| description | We present results on local and boundary regularity for weak solutions to the Navier-Stokes equations. Beginning with the regularity criterion proved recently in [14] for the Cauchy problem, we show that this criterion holds also locally. This is also the case for some other results: We present two examples concerning the regularity of weak solutions stemming from the regularity of two components of the vorticity ([2]) or from the regularity of the pressure ([3]). We conclude by presenting regularity criteria near the boundary based on the results in [10] and [16]. |
| first_indexed | 2024-12-14T04:43:48Z |
| format | Article |
| id | doaj.art-22aa90c462d44fb59575aec73cd7ea75 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-14T04:43:48Z |
| publishDate | 2004-01-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-22aa90c462d44fb59575aec73cd7ea752022-12-21T23:16:44ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912004-01-01200409114Commentary on local and boundary regularity of weak solutions to Navier-Stokes equationsZdenek SkalakWe present results on local and boundary regularity for weak solutions to the Navier-Stokes equations. Beginning with the regularity criterion proved recently in [14] for the Cauchy problem, we show that this criterion holds also locally. This is also the case for some other results: We present two examples concerning the regularity of weak solutions stemming from the regularity of two components of the vorticity ([2]) or from the regularity of the pressure ([3]). We conclude by presenting regularity criteria near the boundary based on the results in [10] and [16].http://ejde.math.txstate.edu/Volumes/2004/09/abstr.htmlNavier-Stokes equationweak solutionpartial regularityenergy inequality. |
| spellingShingle | Zdenek Skalak Commentary on local and boundary regularity of weak solutions to Navier-Stokes equations Electronic Journal of Differential Equations Navier-Stokes equation weak solution partial regularity energy inequality. |
| title | Commentary on local and boundary regularity of weak solutions to Navier-Stokes equations |
| title_full | Commentary on local and boundary regularity of weak solutions to Navier-Stokes equations |
| title_fullStr | Commentary on local and boundary regularity of weak solutions to Navier-Stokes equations |
| title_full_unstemmed | Commentary on local and boundary regularity of weak solutions to Navier-Stokes equations |
| title_short | Commentary on local and boundary regularity of weak solutions to Navier-Stokes equations |
| title_sort | commentary on local and boundary regularity of weak solutions to navier stokes equations |
| topic | Navier-Stokes equation weak solution partial regularity energy inequality. |
| url | http://ejde.math.txstate.edu/Volumes/2004/09/abstr.html |
| work_keys_str_mv | AT zdenekskalak commentaryonlocalandboundaryregularityofweaksolutionstonavierstokesequations |