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

Igor Kukavica; Vlad Vicol

doi:10.1090/S0002-9939-08-09693-7

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

Igor Kukavica, Vlad Vicol

Mathematics

Research output: Contribution to journal › Article › peer-review

75 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 language	English (US)
Pages (from-to)	669-677
Number of pages	9
Journal	Proceedings of the American Mathematical Society
Volume	137
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9939-08-09693-7
State	Published - Feb 2009

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.1090/S0002-9939-08-09693-7

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AB - 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.

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

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