A Regularity Criterion for the Navier-Stokes Equations in the Multiplier Spaces
We exhibit a regularity condition concerning the pressure gradient for the Navier-Stokes equations in a special class. It is shown that if the pressure gradient belongs to 𝐿2/(2−𝑟)̇𝐻((0,𝑇);ℳ(𝑟(ℝ3̇𝐻)→−𝑟(ℝ3))), where ̇𝐻ℳ(𝑟(ℝ3̇𝐻)→−𝑟(ℝ3)) is the multipliers between Sobolev spaces whose definition is giv...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/682436 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832563968297664512 |
|---|---|
| author | Xiang'ou Zhu |
| author_facet | Xiang'ou Zhu |
| author_sort | Xiang'ou Zhu |
| collection | DOAJ |
| description | We exhibit a regularity condition concerning the pressure gradient
for the Navier-Stokes equations in a special class. It is shown that if the pressure
gradient belongs to 𝐿2/(2−𝑟)̇𝐻((0,𝑇);ℳ(𝑟(ℝ3̇𝐻)→−𝑟(ℝ3))), where ̇𝐻ℳ(𝑟(ℝ3̇𝐻)→−𝑟(ℝ3)) is the multipliers between Sobolev spaces whose
definition is given later for 0<𝑟<1, then the Leray-Hopf weak solution to the
Navier-Stokes equations is actually regular. |
| format | Article |
| id | doaj-art-24a3f0daceef4686a4a4e389d6fcc9b9 |
| 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-24a3f0daceef4686a4a4e389d6fcc9b92025-02-03T01:12:09ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/682436682436A Regularity Criterion for the Navier-Stokes Equations in the Multiplier SpacesXiang'ou Zhu0College of Physics and Electronic Information Engineering, Wenzhou University, Zhejiang, Wenzhou 325035, ChinaWe exhibit a regularity condition concerning the pressure gradient for the Navier-Stokes equations in a special class. It is shown that if the pressure gradient belongs to 𝐿2/(2−𝑟)̇𝐻((0,𝑇);ℳ(𝑟(ℝ3̇𝐻)→−𝑟(ℝ3))), where ̇𝐻ℳ(𝑟(ℝ3̇𝐻)→−𝑟(ℝ3)) is the multipliers between Sobolev spaces whose definition is given later for 0<𝑟<1, then the Leray-Hopf weak solution to the Navier-Stokes equations is actually regular.http://dx.doi.org/10.1155/2012/682436 |
| spellingShingle | Xiang'ou Zhu A Regularity Criterion for the Navier-Stokes Equations in the Multiplier Spaces Abstract and Applied Analysis |
| title | A Regularity Criterion for the Navier-Stokes Equations in the Multiplier Spaces |
| title_full | A Regularity Criterion for the Navier-Stokes Equations in the Multiplier Spaces |
| title_fullStr | A Regularity Criterion for the Navier-Stokes Equations in the Multiplier Spaces |
| title_full_unstemmed | A Regularity Criterion for the Navier-Stokes Equations in the Multiplier Spaces |
| title_short | A Regularity Criterion for the Navier-Stokes Equations in the Multiplier Spaces |
| title_sort | regularity criterion for the navier stokes equations in the multiplier spaces |
| url | http://dx.doi.org/10.1155/2012/682436 |
| work_keys_str_mv | AT xiangouzhu aregularitycriterionforthenavierstokesequationsinthemultiplierspaces AT xiangouzhu regularitycriterionforthenavierstokesequationsinthemultiplierspaces |