Ill-posedness of the Navier-Stokes equations in a critical space in 3D
| dc.creator | Bourgain, Jean | |
| dc.creator | Pavlović, Nataša | |
| dc.date | 2008-07-06 | |
| dc.date.accessioned | 2026-07-07T09:48:43Z | |
| dc.date.available | 2026-07-07T09:48:43Z | |
| dc.description | We prove that the Cauchy problem for the three dimensional Navier-Stokes equations is ill posed in $\dot{B}^{-1,\infty}_{\infty}$ in the sense that a ``norm inflation'' happens in finite time. More precisely, we show that initial data in the Schwartz class $\mathcal{S}$ that are arbitrarily small in $\dot{B}^{-1, \infty}_{\infty}$ can produce solutions arbitrarily large in $\dot{B}^{-1, \infty}_{\infty}$ after an arbitrarily short time. Such a result implies that the solution map itself is discontinuous in $\dot{B}^{-1, \infty}_{\infty}$ at the origin. | |
| dc.description | 16 pages, no figures | |
| dc.identifier | https://arxiv.org/abs/0807.0882 | |
| dc.identifier | http://arxiv.org/abs/0807.0882 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/164317 | |
| dc.subject | Analysis of PDEs | |
| dc.title | Ill-posedness of the Navier-Stokes equations in a critical space in 3D | |
| dc.type | text |