Beyond Gevrey regularity

Loss of Gevrey Regularity for Asymptotic Optics

In this paper we will investigate some aspects of the asymptotic behavior of oscillatory integrals from the Gevrey point of view. We will give formal asymptotic expansions and study the Gevrey character of oscillatory integrals, in comparison with the Gevrey character of their amplitudes. We will deduce a formula for the loss of Gevrey regularity both for phase functions in the Morse class and ...

Dissipativity and Gevrey Regularity of a Smoluchowski Equation

We investigate a Smoluchowski equation (a nonlinear Fokker-Planck equation on the unit sphere), which arises in modeling of colloidal suspensions. We prove the dissipativity of the equation in 2D and 3D, in certain Gevrey classes of analytic functions.

Gevrey regularity for a class of water-wave models

MSC: 35Q53 35A07 Keywords: Local well posedness Dispersive smoothing Real-analytic solutions Higher-order water-wave models a b s t r a c t Local well posedness for a class of higher-order nonlinear dispersive partial differential equations is obtained in spaces of functions analytic on a strip around the real axis. The proof relies on estimates in space–time norms adapted to the linear part of...

Gevrey regularity of subelliptic Monge-Ampère equations in the plane

Gevrey Regularity for Navier–stokes Equations under Lions Boundary Conditions

The Navier–Stokes system is considered in a compact Riemannian manifold. Gevrey class regularity is proven under Lions boundary conditions in the cases of the 2D Rectangle, Cylinder, and Hemisphere. The cases of the 2D Sphere and 2D and 3D Torus are also revisited. MSC2010: 35Q30, 76D03