TY - JOUR

T1 - On the radius of analyticity of solutions to the three-dimensional Euler equations

AU - Kukavica, Igor

AU - Vicol, Vlad

N1 - Copyright:
Copyright 2010 Elsevier B.V., All rights reserved.

PY - 2009/2

Y1 - 2009/2

N2 - 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.

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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U2 - 10.1090/S0002-9939-08-09693-7

DO - 10.1090/S0002-9939-08-09693-7

M3 - Article

AN - SCOPUS:70350612106

VL - 137

SP - 669

EP - 677

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 2

ER -