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
Publication statusPublished - 2000 Aug
Externally publishedYes

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Navier-Stokes Equations
Time-periodic Solutions
Small Solutions
Almost Periodic Solution
Exterior Domain
Stationary Solutions
Half-space
Sufficient
Generalise
Sufficient Conditions

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

The Navier-Stokes equations in the weak-Ln space with time-dependent external force. / Yamazaki, Masao.

In: Mathematische Annalen, Vol. 317, No. 4, 08.2000, p. 635-675.

Research output: Contribution to journalArticle

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