On Unique Continuation for Navier-Stokes Equations
We study the unique continuation properties of solutions of the Navier-Stokes equations. We take advantage of rotation transformation of the Navier-Stokes equations to prove the “logarithmic convexity” of certain quantities, which measure the suitable Gaussian decay at infinity to obtain the Gaussia...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2015-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2015/597946 |
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| _version_ | 1832562136397643776 |
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| author | Zhiwen Duan Shuxia Han Peipei Sun |
| author_facet | Zhiwen Duan Shuxia Han Peipei Sun |
| author_sort | Zhiwen Duan |
| collection | DOAJ |
| description | We study the unique continuation properties of solutions of the Navier-Stokes equations. We take advantage of rotation transformation of the Navier-Stokes equations to prove the “logarithmic convexity” of certain quantities, which measure the suitable Gaussian decay at infinity to obtain the Gaussian decay weighted estimates, as well as Carleman inequality. As a consequence we obtain sufficient conditions on the behavior of the solution at two different times t0=0 and t1=1 which guarantee the “global” unique continuation of solutions for the Navier-Stokes equations. |
| format | Article |
| id | doaj-art-dfc3e7a5726341db8f36b3fc0be96420 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-dfc3e7a5726341db8f36b3fc0be964202025-02-03T01:23:26ZengWileyAbstract and Applied Analysis1085-33751687-04092015-01-01201510.1155/2015/597946597946On Unique Continuation for Navier-Stokes EquationsZhiwen Duan0Shuxia Han1Peipei Sun2Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074, ChinaDepartment of Mathematics, Huazhong University of Science and Technology, Wuhan 430074, ChinaDepartment of Mathematics, Huazhong University of Science and Technology, Wuhan 430074, ChinaWe study the unique continuation properties of solutions of the Navier-Stokes equations. We take advantage of rotation transformation of the Navier-Stokes equations to prove the “logarithmic convexity” of certain quantities, which measure the suitable Gaussian decay at infinity to obtain the Gaussian decay weighted estimates, as well as Carleman inequality. As a consequence we obtain sufficient conditions on the behavior of the solution at two different times t0=0 and t1=1 which guarantee the “global” unique continuation of solutions for the Navier-Stokes equations.http://dx.doi.org/10.1155/2015/597946 |
| spellingShingle | Zhiwen Duan Shuxia Han Peipei Sun On Unique Continuation for Navier-Stokes Equations Abstract and Applied Analysis |
| title | On Unique Continuation for Navier-Stokes Equations |
| title_full | On Unique Continuation for Navier-Stokes Equations |
| title_fullStr | On Unique Continuation for Navier-Stokes Equations |
| title_full_unstemmed | On Unique Continuation for Navier-Stokes Equations |
| title_short | On Unique Continuation for Navier-Stokes Equations |
| title_sort | on unique continuation for navier stokes equations |
| url | http://dx.doi.org/10.1155/2015/597946 |
| work_keys_str_mv | AT zhiwenduan onuniquecontinuationfornavierstokesequations AT shuxiahan onuniquecontinuationfornavierstokesequations AT peipeisun onuniquecontinuationfornavierstokesequations |