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

Matthias Georg Hieber, Okihiro Sawada

Research output: Contribution to journalArticle

41 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)269-285
Number of pages17
JournalArchive for Rational Mechanics and Analysis
Volume175
Issue number2
DOIs
Publication statusPublished - 2005 Feb
Externally publishedYes

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Navier-Stokes
Navier Stokes equations
Navier-Stokes Equations
Semigroup
Linearly
Local Solution
Mild Solution
Stokes
Form

ASJC Scopus subject areas

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

Cite this

The Navier-Stokes equations in ℝn with linearly growing initial data. / Hieber, Matthias Georg; Sawada, Okihiro.

In: Archive for Rational Mechanics and Analysis, Vol. 175, No. 2, 02.2005, p. 269-285.

Research output: Contribution to journalArticle

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