Originally motivated by a stability problem in Fluid Mechanics, we study the spectral and pseudospectral properties of the differential operator HÇ« = âˆ’âˆ‚2 x + x + iÇ«f(x) on L(R), where f is aâ€¦ (More)

We give a condition for the periodic, three dimensional, incompressible Navier-Stokes equations to be globally wellposed. This condition is not a smallness condition on the initial data, as the dataâ€¦ (More)

â€” We are interested in a model of rotating fluids, describing the motion of the ocean in the equatorial zone. This model is known as the Saint-Venant, or shallow-water type system, to which aâ€¦ (More)

We provide a rigorous derivation of the brownian motion as the limit of a deterministic system of hard-spheres as the number of particles N goes to infinity and their diameter Îµ simultaneously goesâ€¦ (More)

In [4]-[6] classes of initial data to the three dimensional, incompressible NavierStokes equations were presented, generating a global smooth solution although the norm of the initial data may beâ€¦ (More)

We propose two different proofs of the fact that Oseenâ€™s vortex is the unique solution of the two-dimensional Navier-Stokes equation with a Dirac mass as initial vorticity. The first argument, due toâ€¦ (More)

â€” A class of pseudodifferential operators on the Heisenberg group is defined. As it should be, this class is an algebra containing the class of differential operators. Furthermore, thoseâ€¦ (More)

(2013) A profile decomposition approach to the Lâˆž/t (L3/ x) Navierâ€“Stokes regularity criterion. Mathematische Annalen, 355 (4). This document is made available in accordance with publisher policiesâ€¦ (More)