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

Igor Kukavica, Vlad Vicol

Research output: Contribution to journalArticlepeer-review

62 Scopus citations

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 2009

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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