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.
All Science Journal Classification (ASJC) codes
- General Mathematics
- Applied Mathematics