The Navier-Stokes equations in ℝn with linearly growing initial data

Matthias Georg Hieber, Okihiro Sawada

研究成果: Article査読

45 被引用数 (Scopus)

抄録

Consider the equations of Navier-Stokes on ℝn with initial data U0 of the form U0(x) = u0(x) - Mx, where M is an n x n matrix with constant real entries and u0 ∈ L σ p(ℝn). It is shown that under these assumptions the equations of Navier-Stokes admit a unique local solution in Lσ p(ℝn). Moreover, if ∥e tM∥ ≦ 1 for all t ≧ 0, then this mild solution is even analytic in x. This is surprising since the underlying semigroup of Ornstein-Uhlenbeck type is not analytic, in contrast to the Stokes semigroup.

本文言語English
ページ(範囲)269-285
ページ数17
ジャーナルArchive for Rational Mechanics and Analysis
175
2
DOI
出版ステータスPublished - 2005 2
外部発表はい

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mathematics(all)
  • Mathematics (miscellaneous)

フィンガープリント 「The Navier-Stokes equations in ℝn with linearly growing initial data」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル