Space-time analyticity and refined analyticity radius of the Navier-Stokes equations in the critical Besov spaces
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916644473798656 |
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| author | Wang, Cong |
| author_facet | Wang, Cong |
| contents | In this paper, we establish the space-time analyticity of global solutions to the incompressible Navier-Stokes equations with small initial data in critical \emph{Besov} spaces $\dot B^{3/p-1}_{p,q}$. Time decay rates of higher order space-time joint derivatives and instantaneous lower bounds of the analyticity radius follow as straightforward consequences. The method employed combines Gevrey-class estimates with iterative derivative techniques. Furthermore, we obtain a logarithmic improvement in the lower bound for the spatial analyticity radius of solutions for arbitrary initial data in critical \emph{Besov} spaces. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_03658 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Space-time analyticity and refined analyticity radius of the Navier-Stokes equations in the critical Besov spaces Wang, Cong Analysis of PDEs In this paper, we establish the space-time analyticity of global solutions to the incompressible Navier-Stokes equations with small initial data in critical \emph{Besov} spaces $\dot B^{3/p-1}_{p,q}$. Time decay rates of higher order space-time joint derivatives and instantaneous lower bounds of the analyticity radius follow as straightforward consequences. The method employed combines Gevrey-class estimates with iterative derivative techniques. Furthermore, we obtain a logarithmic improvement in the lower bound for the spatial analyticity radius of solutions for arbitrary initial data in critical \emph{Besov} spaces. |
| title | Space-time analyticity and refined analyticity radius of the Navier-Stokes equations in the critical Besov spaces |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2503.03658 |