Global solution of the 3D incompressible Navier–Stokes equations in the Besov spaces x" xmlns:search="http://marklogic.com/appservices/search">\({\dot{\varvec{R}}}_{{\varvec{r}}_{\varvec{1}},{\varvec{r}}_{{\varvec{2}}},{\varvec{r}}_{{\varvec{3}}
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- 作者：Shaolei Ru ; Jiecheng Chen
- 关键词：Navier–Stokes equations ; Global well ; posedness ; Critical spaces
- 刊名：Zeitschrift für angewandte Mathematik und Physik
- 出版年：2017
- 出版时间：April 2017
- 年：2017
- 卷：68
- 期：2
- 全文大小：
- 刊物主题：Theoretical and Applied Mechanics; Mathematical Methods in Physics;
- 出版者：Springer International Publishing
- ISSN：1420-9039
- 卷排序：68
文摘
In this paper, we construct a more general Besov spaces \(\dot{R}_{r_{1},r_{2},r_{3}}^{\sigma ,q}\) and consider the global well-posedness of incompressible Navier–Stokes equations with small data in \(\dot{R}_{r_{1},r_{2},r_{3}}^{\sigma ,1}\) for \(\frac{1}{r_{1}}+\frac{1}{r_{2}}+\frac{1}{r_{3}}-\sigma =1\), \(1\leqslant r_{i}<\infty \) and \(\max \limits _{1\leqslant i\leqslant 3}r_{i}\leqslant 2\min \limits _{1\leqslant i\leqslant 3}r_{i}\). In particular, by studying the well-posedness of incompressible Navier–Stokes equations in \(\dot{R}_{r_{1},r_{2},r_{3}}^{\sigma ,1}\), we can explore the relationship between \(u_{1}(x,t)\), \(u_{2}(x,t)\) and \(u_{3}(x,t)\) in u(x, t).