The Navier-Stokes equations in the weak-Ln space with time-dependent external force

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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 n ≥ 3. We give conditions on the external force sufficient for the unique existence of small solutions in the weak-Ln 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-Ln space with time-independent external force.

Original languageEnglish
Pages (from-to)635-675
Number of pages41
JournalMathematische Annalen
Volume317
Issue number4
DOIs
Publication statusPublished - 2000 Aug

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ASJC Scopus subject areas

  • Mathematics(all)

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