On the radius of analyticity of solutions to the three-dimensional Euler equations

Igor Kukavica, Vlad Vicol

Research output: Contribution to journalArticle

Abstract

We address the problem of analyticity of smooth solutions u of the incompressible Euler equations. If the initial datum is real-analytic, the solution remains real-analytic as long as ∫t0 ∥∇ u(-,s) ∥L∞ ds < ∞.Using a Gevrey-class approach we obtain lower bounds on the radius of space analyticity which depend algebraically on exp ∫t0 ∥∇u(·,s)∥L∞ds.In particular, we answer in the positive a question posed by Levermore and Oliver.

Original languageEnglish (US)
Pages (from-to)669-677
Number of pages9
JournalProceedings of the American Mathematical Society
Volume137
Issue number2
DOIs
StatePublished - Feb 1 2009

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Euler equations
Analyticity
Euler Equations
Radius
Gevrey Classes
Incompressible Euler Equations
Three-dimensional
Smooth Solution
Lower bound

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

On the radius of analyticity of solutions to the three-dimensional Euler equations. / Kukavica, Igor; Vicol, Vlad.

In: Proceedings of the American Mathematical Society, Vol. 137, No. 2, 01.02.2009, p. 669-677.

Research output: Contribution to journalArticle

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