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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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 1085-3375 1687-0409 |