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: Jaiok Roh
Format: Article
Language:English
Published: Wiley 2011-01-01
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.
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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