On the initial value problem for the Navier-Stokes equations with the initial datum in the Sobolev spaces

Thời gian: 10:00 đến 11:30 Ngày 02/11/2016

Địa điểm: B4-705

Tóm tắt:

In this talk, we introduce some results on local well-posedness for the Navier-Stokes equations with arbitrary initial data
in homogeneous Sobolev spaces $\dot{H}^s_p(\mathbb{R}^d)$ for $d \geq 2, p > \frac{d}{2},\ {\rm and}\ \frac{d}{p} - 1 \leq s < \frac{d}{2p}$.
The obtained result improves the known ones for $p > d$ and $s = 0$ M. Cannone (1995) . In the case of critical indexes $s=\frac{d}{p}-1$,
we prove global well-posedness for Navier-Stokes equations when the norm of the initial value is small enough. This result is a generalization of the one in M.
Cannone (1997) in which $p = d$ and $s = 0$.