Besov mixed-Morrey spaces: On an Application to the Navier-Stokes Equations
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918078263066624 |
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| author | Aurazo-Alvarez, Leithold L. Neves, Wladimir |
| author_facet | Aurazo-Alvarez, Leithold L. Neves, Wladimir |
| contents | In this paper we introduce two new classes of functional spaces, namely, Besov mixed-Morrey spaces and Fourier-Besov mixed-Morrey spaces, and then we establish some basic properties for these classes. Moreover, we explore the d-dimensional incompressible Navier-Stokes equations in this context, by mean of a Bony's paraproduct approach, in order to get the global well-posedness for small initial data. These results provides a new class of initial data with a sort of anisotropy in relation to its spatial variables or frequency variables. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_00970 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Besov mixed-Morrey spaces: On an Application to the Navier-Stokes Equations Aurazo-Alvarez, Leithold L. Neves, Wladimir Analysis of PDEs In this paper we introduce two new classes of functional spaces, namely, Besov mixed-Morrey spaces and Fourier-Besov mixed-Morrey spaces, and then we establish some basic properties for these classes. Moreover, we explore the d-dimensional incompressible Navier-Stokes equations in this context, by mean of a Bony's paraproduct approach, in order to get the global well-posedness for small initial data. These results provides a new class of initial data with a sort of anisotropy in relation to its spatial variables or frequency variables. |
| title | Besov mixed-Morrey spaces: On an Application to the Navier-Stokes Equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2507.00970 |