Paolo Maremonti

Stabilità asintotica in media per moti fluidi viscosi in domini esterni

SummaryIn this paper we prove some asymptotic stability results for Navier-Stokes fluid filling an exterior domain. In particular, we show that if the Reynolds number associated to the basic flow is sufficiently small, then the energy of perturbations tends to zero as t→∞,provided only that the energy is finite at t=0.This result also solves, as a special case, a problem pointed out by J. Leray in [25].

On the spatial asymptotic decay of a suitable weak solution to the Navier-Stokes Cauchy problem

We prove space–time decay estimates of suitable weak solutions to the Navier–Stokes Cauchy problem, corresponding to a given asymptotic behavior of the initial data of the same order of decay. We use two main tools. The first is a result obtained in [7] for the behavior of the solution in a neighborhood of t = 0 in the -norm, which enables us to furnish a representation formula for a suitable weak solution. The second is the asymptotic behavior of for . Following Lerays point of view, roughly speaking our result proves that a possible space–time turbulence does not perturb the asymptotic spatial behavior of the initial data of a suitable weak solution.

Global Existence of Solutions to 2-D Navier–Stokes Flow with Non-decaying Initial Data in Exterior Domains

We study the two dimensional Navier–Stokes initial boundary value problem in exterior domains assuming that the initial data

An Interpolation Inequality in Exterior Domains.

u_0

On the Navier–Stokes Problem in Exterior Domains with Non Decaying Initial Data

u0 belongs

Higher regularity of solutions to the singular

L^\infty