Gevrey Regularity of Solutions to the 3D Navier-Stokes Equations

摘要

We consider local existence and Gevrey regularity of solutions to the Navier-Stokes equations for a three dimensional periodic homogeneous incompressible flow. Existence and regularity are established for initial data whose Fourier coefficients belong to suitable sequence spaces. The proof uses Banach space methods and in particular does not rely on energy or enstrophy estimates.