On the initial value problem for the Navier-Stokes equations with the initial datum in the Sobolev spaces
| Autor: | Khai, D. Q., Duong, V. T. T. |
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| Rok vydání: | 2016 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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 $d \geq 2, p > \frac{d}{2},\ {\rm and}\ \frac{d}{p} - 1 \leq s < \frac{d}{2p}$. 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. Comment: 18pages. arXiv admin note: text overlap with arXiv:1603.01896 |
| Databáze: | arXiv |
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