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Article overview
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On the initial value problem for the Navier-Stokes equations with the initial datum in the Sobolev spaces | D. Q. Khai
; V. T. T. Duong
; | Date: |
14 Mar 2016 | Abstract: | In this paper, we study local well-posedness for the Navier-Stokes equations
with arbitrary initial data in homogeneous Sobolev spaces
$dot{H}^s_p(mathbb{R}^d)$ for $d geq 2, p > frac{d}{2}, {
m and}
frac{d}{p} - 1 leq s < frac{d}{2p}$. The obtained result improves the known
ones for $p > d$ and $s = 0$ (see M. Cannone (1995), M. Cannone and Y. Meyer
(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 ones in Cannone (1999)
and P. G. Lemarie-Rieusset (2002) in which $(p = d, s = 0)$ and $(p > d, s =
frac{d}{p} - 1)$, respectively. | Source: | arXiv, 1603.4219 | Services: | Forum | Review | PDF | Favorites |
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