ð ¿ ð ‘Ÿ - ð ¿ ð ‘ Stability of the Incompressible Flows with Nonzero Far-Field Velocity

Jaiok Roh

Abstract and Applied Analysis, 2011, vol. 2011, 1-15

Abstract:

We consider the stability of stationary solutions ð ° for the exterior Navier-Stokes flows with a nonzero constant velocity ð ® âˆž at infinity. For ð ® âˆž = 0 with nonzero stationary solution ð ° , Chen (1993), Kozono and Ogawa (1994), and Borchers and Miyakawa (1995) have studied the temporal stability in ð ¿ ð ‘ spaces for 1 < ð ‘ and obtained good stability decay rates. For the spatial direction, we recently obtained some results. For ð ® âˆž ≠0 , Heywood (1970, 1972) and Masuda (1975) have studied the temporal stability in ð ¿ 2 space. Shibata (1999) and Enomoto and Shibata (2005) have studied the temporal stability in ð ¿ ð ‘ spaces for ð ‘ â‰¥ 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 ð ¿ ð ‘ for ð ‘ > 1 and obtain ð ¿ ð ‘Ÿ - ð ¿ ð ‘ stability as Kozono and Ogawa and Borchers and Miyakawa obtained for ð ® âˆž = 0 .

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:856896

DOI: 10.1155/2011/856896

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