About the regularized Navier--Stokes equations
| dc.creator | Cannone, Marco | |
| dc.creator | Karch, Grzegorz | |
| dc.date | 2003-05-06 | |
| dc.date.accessioned | 2026-07-07T04:57:48Z | |
| dc.date.available | 2026-07-07T04:57:48Z | |
| dc.description | The first goal of this paper is to study the large time behavior of solutions to the Cauchy problem for the 3-dimensional incompressible Navier-Stokes system. The Marcinkiewicz space $L^{3,\infty}$ is used to prove some asymptotic stability results for solutions with infinite energy. Next, this approach is applied to the analysis of two classical ``regularized'' Navier-Stokes systems. The first one was introduced by J. Leray and consists in ``mollifying'' the nonlinearity. The second one was proposed by J.L. Lions, who added the artificial hyper-viscosity $(-Δ)^{\ell/2}$, $\ell>2$, to the model. It is shown in the present paper that, in the whole space, solutions to those modified models converge as $t\to\infty$ toward solutions of the original Navier-Stokes system. | |
| dc.identifier | https://arxiv.org/abs/math/0305097 | |
| dc.identifier | http://arxiv.org/abs/math/0305097 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67389 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35Q30; 76D05; 35B40 | |
| dc.title | About the regularized Navier--Stokes equations | |
| dc.type | text |