Microlocal smoothing effect for Schrödinger equations in Gevrey spaces

Gevrey Class Smoothing Effect for the Prandtl Equation

A remark on the Schrödinger smoothing effect

— We prove the equivalence between the smoothing effect for a Schrödinger operator and the decay of the associate spectral projectors. We give two applications to the Schrödinger operator in dimension one. Résumé. — On donne une caractérisation de l’effet régularisant pour un opérateur de Schrödinger par la décroissance de ses projecteurs spectraux. On en déduit deux applications à l’opérateur ...

Asymptotic expansion in Gevrey spaces for solutions of Navier-Stokes equations

In this paper, we study the asymptotic behavior of solutions to the threedimensional incompressible Navier-Stokes equations (NSE) with periodic boundary conditions and potential body forces. In particular, we prove that the Foias-Saut asymptotic expansion for the regular solutions of the NSE in fact holds in all Gevrey classes . This strengthens the previous result obtained in Sobolev spaces by...

Smoothing properties of stochastic equations in Hilbert spaces

A nonlinear stochastic equation in a Hilbert space is considered, with constant but possibly degenerate diiusion term. Some smoothing properties for the associated transition semigroup are studied. In particular, strong Feller property and irreducibility are proved. The main tools are Malliavin calculus and Girsanov transformation.

Two-microlocal Spaces, Local Norms, and Weighted Spaces

We generalize the two-microlocal spaces of Bony to a Triebel-Lizorkin setting, which includes HH older and general Sobolev type spaces as special cases, and prove that these spaces can be characterized by size estimates on wavelet coeecients. Using this characterization we then prove two alternative characterizations of the new spaces, where the rst one involves local norms and the second one r...