Calcul pseudo-différentiel et équations d'évolution non linéaires sur les variétés compactes

Abstract

By using the pseudo-differential and para-differential calculus introduced by J.-M. Bony [1], we study the incompressible isotropic Navier–Stokes equations. We prove the short-time existence and uniqueness of solutions for arbitrary data with supercritical regularity. We exploit pseudo-differential calculus to extend the analysis to compact Riemannian manifolds.