On Some Regularity Criteria for Axisymmetric Navier–Stokes Equations
We point out some criteria that imply regularity of axisymmetric solutions to Navier–Stokes equations. We show that boundedness of ‖ v r / r 3 ‖ L 2 ( R 3 × ( 0 , T ) ) as well as boundedness of ‖ ω φ / r ‖ L 2 ( R 3 × ( 0 , T ) ) , where v r is the radial component of velocity and ω φ is the angula...
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| Veröffentlicht in: | Journal of mathematical fluid mechanics 2019-12, Vol.21 (4), p.1-14, Article 51 |
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| container_title | Journal of mathematical fluid mechanics |
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| creator | Rencławowicz, Joanna Zaja̧czkowski, Wojciech M. |
| description | We point out some criteria that imply regularity of axisymmetric solutions to Navier–Stokes equations. We show that boundedness of
‖
v
r
/
r
3
‖
L
2
(
R
3
×
(
0
,
T
)
)
as well as boundedness of
‖
ω
φ
/
r
‖
L
2
(
R
3
×
(
0
,
T
)
)
, where
v
r
is the radial component of velocity and
ω
φ
is the angular component of vorticity, imply regularity of weak solutions. |
| doi_str_mv | 10.1007/s00021-019-0447-0 |
| format | Article |
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‖
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as well as boundedness of
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‖
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v
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/
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3
‖
L
2
(
R
3
×
(
0
,
T
)
)
as well as boundedness of
‖
ω
φ
/
r
‖
L
2
(
R
3
×
(
0
,
T
)
)
, where
v
r
is the radial component of velocity and
ω
φ
is the angular component of vorticity, imply regularity of weak solutions.</description><subject>Angular velocity</subject><subject>Classical and Continuum Physics</subject><subject>Fluid dynamics</subject><subject>Fluid flow</subject><subject>Fluid mechanics</subject><subject>Fluid- and Aerodynamics</subject><subject>Mathematical analysis</subject><subject>Mathematical Methods in Physics</subject><subject>Navier-Stokes equations</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Regularity</subject><subject>Theoretical mathematics</subject><subject>Vorticity</subject><issn>1422-6928</issn><issn>1422-6952</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><sourceid>C6C</sourceid><recordid>eNp1kMFOwzAMhiMEEmPwANwqcS7YSds0x2naGNLEJAbnKO3SKWNttqRF7MY78IY8CZmK4MTF9uH7besj5BrhFgH4nQcAijGgiCFJeAwnZIAJpXEmUnr6O9P8nFx4vwFAngo6INNFEy1traMnve62ypn2EI1D1c6oqLIuGr0bf6hr3TpTRo_qzWj39fG5bO2r9tFk36nW2MZfkrNKbb2--ulD8jKdPI9n8Xxx_zAezeOSiayNyzwtkAnNM85UCgXSQmOpcy40SyhWqqiAqlURni2rVZVAgoyxjEMRUEgEG5Kbfu_O2X2nfSs3tnNNOCkpzXmKIscjhT1VOuu905XcOVMrd5AI8qhL9rpk0CWPuiSEDO0zPrDNWru_zf-HvgGNDG1B</recordid><startdate>20191201</startdate><enddate>20191201</enddate><creator>Rencławowicz, Joanna</creator><creator>Zaja̧czkowski, Wojciech M.</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>C6C</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20191201</creationdate><title>On Some Regularity Criteria for Axisymmetric Navier–Stokes Equations</title><author>Rencławowicz, Joanna ; Zaja̧czkowski, Wojciech M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c396t-c85b139e7673a50b12be1ce879e3421fabf02adb422cfdf4041333670bb120493</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Angular velocity</topic><topic>Classical and Continuum Physics</topic><topic>Fluid dynamics</topic><topic>Fluid flow</topic><topic>Fluid mechanics</topic><topic>Fluid- and Aerodynamics</topic><topic>Mathematical analysis</topic><topic>Mathematical Methods in Physics</topic><topic>Navier-Stokes equations</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Regularity</topic><topic>Theoretical mathematics</topic><topic>Vorticity</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Rencławowicz, Joanna</creatorcontrib><creatorcontrib>Zaja̧czkowski, Wojciech M.</creatorcontrib><collection>Springer Nature OA Free Journals</collection><collection>CrossRef</collection><jtitle>Journal of mathematical fluid mechanics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Rencławowicz, Joanna</au><au>Zaja̧czkowski, Wojciech M.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On Some Regularity Criteria for Axisymmetric Navier–Stokes Equations</atitle><jtitle>Journal of mathematical fluid mechanics</jtitle><stitle>J. Math. Fluid Mech</stitle><date>2019-12-01</date><risdate>2019</risdate><volume>21</volume><issue>4</issue><spage>1</spage><epage>14</epage><pages>1-14</pages><artnum>51</artnum><issn>1422-6928</issn><eissn>1422-6952</eissn><abstract>We point out some criteria that imply regularity of axisymmetric solutions to Navier–Stokes equations. We show that boundedness of
‖
v
r
/
r
3
‖
L
2
(
R
3
×
(
0
,
T
)
)
as well as boundedness of
‖
ω
φ
/
r
‖
L
2
(
R
3
×
(
0
,
T
)
)
, where
v
r
is the radial component of velocity and
ω
φ
is the angular component of vorticity, imply regularity of weak solutions.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s00021-019-0447-0</doi><tpages>14</tpages><oa>free_for_read</oa></addata></record> |
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| issn | 1422-6928 1422-6952 |
| language | eng |
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| source | SpringerLink Journals - AutoHoldings |
| subjects | Angular velocity Classical and Continuum Physics Fluid dynamics Fluid flow Fluid mechanics Fluid- and Aerodynamics Mathematical analysis Mathematical Methods in Physics Navier-Stokes equations Physics Physics and Astronomy Regularity Theoretical mathematics Vorticity |
| title | On Some Regularity Criteria for Axisymmetric Navier–Stokes Equations |
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