The Probabilistic Method and large initial data for Generalized Navier-Stokes systems

Abstract

In this paper we introduce a probabilistic approach to show the existence of initial data with arbitrarily large $L^2({\mathbb{R}}^3)$, ${\dot{H}}^{1/2}({\mathbb{R}}^3)$ and ${\mathcal{P}\mathcal{M}}^2$-norms for which a Generalized Navier-Stokes system generate a global regular solution. More precisely, we show that from a certain family of possible large initial data most of them give raise to global regular solutions to a given Generalized Navier-Stokes system.

21 pages. A better discussion on the probabilistic setting has been included. Conditions on the initial data, as the divergence free condition and real-valuedness, have been taken care of. A section on how the arguments can be generalized has been added

References in corpus (3)

• On the global wellposedness of the 3-D Navier-Stokes equations with large initial data
• Random-data Cauchy Problem for the Periodic Navier-Stokes Equations with Initial Data in Negative-order Sobolev Spaces
• An addendum to the paper: "Some elementary estimates for the Navier-Stokes system"