Weak solutions of the Navier-Stokes equations with non-zero boundary values in an exterior domain satisfying the strong energy inequality

Reinhard Farwig, Hideo Kozono

研究成果: Article査読

7 被引用数 (Scopus)

抄録

In an exterior domain Ω⊂R3 and a time interval [0, T), 0<T≤∞, consider the instationary Navier-Stokes equations with initial value u0∈Lσ2(Ω) and external force f=divF, F∈L2(0, T;L2(Ω)). As is well-known there exists at least one weak solution in the sense of J. Leray and E. Hopf with vanishing boundary values satisfying the strong energy inequality. In this paper, we extend the class of global in time Leray-Hopf weak solutions to the case when u=g with non-zero time-dependent boundary values g. Although uniqueness for these solutions cannot be proved, we show the existence of at least one weak solution satisfying the strong energy inequality and a related energy estimate.

本文言語English
ページ(範囲)2633-2658
ページ数26
ジャーナルJournal of Differential Equations
256
7
DOI
出版ステータスPublished - 2014 4 1
外部発表はい

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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