TY - JOUR
T1 - On the radius of analyticity of solutions to the three-dimensional Euler equations
AU - Kukavica, Igor
AU - Vicol, Vlad
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
SN - 0002-9939
VL - 137
SP - 669
EP - 677
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 2
ER -