On the local Smoothness of Solutions of the Navier-Stokes Equations
| dc.creator | Dong, Hongjie | |
| dc.creator | Du, Dapeng | |
| dc.date | 2005-02-05 | |
| dc.date.accessioned | 2026-07-07T05:16:43Z | |
| dc.date.available | 2026-07-07T05:16:43Z | |
| dc.description | We consider the Cauchy problem for incompressible Navier-Stokes equations $u_t+u\nabla_xu-Δu+\nabla p=0, div u=0 in R^d \times R^+$ with initial data $a\in L^d(R^d)$, and study in some detail the smoothing effect of the equation. We prove that for $T<\infty$ and for any positive integers $n$ and $m$ we have $t^{m+n/2}D^m_tD^{n}_x u\in L^{d+2}(R^d\times (0,T))$, as long as the $\|u\|_{L^{d+2}_{x,t}(R^d\times (0,T))}$ stays finite. | |
| dc.description | 14 pages | |
| dc.identifier | https://arxiv.org/abs/math/0502104 | |
| dc.identifier | http://arxiv.org/abs/math/0502104 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74089 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35Q30; 76D03; 76D05 | |
| dc.title | On the local Smoothness of Solutions of the Navier-Stokes Equations | |
| dc.type | text |