The Navier-Stokes equations in the weak-
LnL^n space with time-dependent external force |
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Authors: | Masao Yamazaki |
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Institution: | (1) Department of Mathematics, Hitotsubashi University, Kunitachi, Tokyo 186-8601, Japan (e-mail: cc00053@srv.cc.hit-u.ac.jp) , JP |
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Abstract: | Abstract. We consider the Navier-Stokes equations with time-dependent external force, either in the whole time or in positive time
with initial data, with domain either the whole space, the half space or an exterior domain of dimension . We give conditions on the external force sufficient for the unique existence of small solutions in the weak- space bounded for all time. In particular, this result gives sufficient conditions for the unique existence and the stability
of small time-periodic solutions or almost periodic solutions. This result generalizes the previous result on the unique existence
and the stability of small stationary solutions in the weak- space with time-independent external force.
Received: 30 March 1999 / Accepted: 21 September 1999 / Published online: 28 June 2000 |
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Keywords: | Mathematics Subject Classification (2000): 35Q30 35B10 35B15 46G10 |
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