# Global well-posedness for the incompressible Navier–Stokes equations in the critical Besov space under the Lagrangian coordinates

Takayoshi Ogawa, Senjo Shimizu

1 被引用数 (Scopus)

## 抄録

We consider global well-posedness of the Cauchy problem of the incompressible Navier–Stokes equations under the Lagrangian coordinates in scaling critical Besov spaces. We prove the system is globally well-posed in the homogeneous Besov space B˙p,1−1+n/p(Rn) with 1≤p<∞. The former result was restricted for 1≤p<2n and the main reason why the well-posedness space is enlarged is that the quasi-linear part of the system has a special feature called a multiple divergence structure and the bilinear estimate for the nonlinear terms are improved by such a structure. Our result indicates that the Navier–Stokes equations can be transferred from the Eulerian coordinates to the Lagrangian coordinates even for the solution in the limiting critical Besov spaces.

本文言語 English 613-651 39 Journal of Differential Equations 274 https://doi.org/10.1016/j.jde.2020.10.023 Published - 2021 2 15

• 分析
• 応用数学

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