Well-Posedness for the Navier-Stokes Equations with Datum in the Sobolev Spaces

被引：3

作者：

Khai D.Q. ^{[1
]}

机构：

[1] Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Cau Giay, 10307, Hanoi

来源：

Acta Mathematica Vietnamica | 2017年 / 42卷 / 3期

关键词：

Critical Sobolev and Besov spaces; Existence and uniqueness of local and global mild solutions; Navier-Stokes equations;

D O I：

10.1007/s40306-016-0192-x

中图分类号：

学科分类号：

摘要：

In this paper, we study local well-posedness for the Navier-Stokes equations with arbitrary initial data in homogeneous Sobolev spaces Ḣps(ℝd) for d≥2,p>d2, and dp−1≤s<d2p. The obtained result improves the known ones for p > d and s = 0 (see [4, 6]). In the case of critical indexes s=dp−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 [5] in which p = d and s = 0. © 2016, Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore.

引用

页码：431 / 443

页数：12

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