Lr-Lp Stability of the Incompressible Flows with Nonzero Far-Field Velocity
We consider the stability of stationary solutions w for the exterior Navier-Stokes flows with a nonzero constant velocity u∞ at infinity. For u∞=0 with nonzero stationary solution w, Chen (1993), Kozono and Ogawa (1994), and Borchers and Miyakawa (1995) have studied the temporal stability in Lp spac...
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Wiley
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/856896 |
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| author | Jaiok Roh |
| author_facet | Jaiok Roh |
| author_sort | Jaiok Roh |
| collection | DOAJ |
| description | We consider the stability of stationary solutions w for the exterior Navier-Stokes flows with a nonzero constant velocity u∞ at infinity. For u∞=0 with nonzero stationary solution w, Chen (1993), Kozono and Ogawa (1994), and Borchers and Miyakawa (1995) have studied the temporal stability in Lp spaces for 1<p and obtained good stability decay rates. For the spatial direction, we recently obtained some results. For u∞≠0, Heywood (1970, 1972) and Masuda (1975) have studied the temporal stability in L2 space. Shibata (1999) and Enomoto and Shibata (2005) have studied the temporal stability in Lp spaces for p≥3. Then, Bae and Roh recently improved Enomoto and Shibata's results in some sense. In this paper, we improve Bae and Roh's result in the spaces Lp for p>1 and obtain Lr-Lp stability as Kozono and Ogawa and Borchers and Miyakawa obtained for u∞=0. |
| format | Article |
| id | doaj-art-67de5b20c0ea4d7b9dcfb759761616c1 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-67de5b20c0ea4d7b9dcfb759761616c12025-08-20T03:34:01ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/856896856896Lr-Lp Stability of the Incompressible Flows with Nonzero Far-Field VelocityJaiok Roh0Department of Mathematics, Hallym University, Chuncheon 200-702, Republic of KoreaWe consider the stability of stationary solutions w for the exterior Navier-Stokes flows with a nonzero constant velocity u∞ at infinity. For u∞=0 with nonzero stationary solution w, Chen (1993), Kozono and Ogawa (1994), and Borchers and Miyakawa (1995) have studied the temporal stability in Lp spaces for 1<p and obtained good stability decay rates. For the spatial direction, we recently obtained some results. For u∞≠0, Heywood (1970, 1972) and Masuda (1975) have studied the temporal stability in L2 space. Shibata (1999) and Enomoto and Shibata (2005) have studied the temporal stability in Lp spaces for p≥3. Then, Bae and Roh recently improved Enomoto and Shibata's results in some sense. In this paper, we improve Bae and Roh's result in the spaces Lp for p>1 and obtain Lr-Lp stability as Kozono and Ogawa and Borchers and Miyakawa obtained for u∞=0.http://dx.doi.org/10.1155/2011/856896 |
| spellingShingle | Jaiok Roh Lr-Lp Stability of the Incompressible Flows with Nonzero Far-Field Velocity Abstract and Applied Analysis |
| title | Lr-Lp Stability of the Incompressible Flows with Nonzero Far-Field Velocity |
| title_full | Lr-Lp Stability of the Incompressible Flows with Nonzero Far-Field Velocity |
| title_fullStr | Lr-Lp Stability of the Incompressible Flows with Nonzero Far-Field Velocity |
| title_full_unstemmed | Lr-Lp Stability of the Incompressible Flows with Nonzero Far-Field Velocity |
| title_short | Lr-Lp Stability of the Incompressible Flows with Nonzero Far-Field Velocity |
| title_sort | lr lp stability of the incompressible flows with nonzero far field velocity |
| url | http://dx.doi.org/10.1155/2011/856896 |
| work_keys_str_mv | AT jaiokroh lrlpstabilityoftheincompressibleflowswithnonzerofarfieldvelocity |