The Radius of Analyticity of Solutions to the Three-Dimensional Euler Equations
by
Vlad Vicol
University of Southern California
Coauthors: Igor Kukavica (University of Southern California)

We address the problem of analyticity and Gevrey-regularity of smooth solutions u of the incompressible Euler equations. If the initial datum is real-analytic, the solution remains real-analytic as long as ∫₀^t ∥∇u(·, s)∥_L^∞ ds < ∞ (cf. Bardos and Benachour). In the periodic case, using a Fourier method, we obtain a lower bound on the uniform radius of space analyticity which depends algebraically on exp∫₀^t ∥∇u(·, s)∥_L^∞ds. In particular, we positively answer a question posed by Levermore and Oliver.

Date received: July 8, 2008