Global well-posedness of the Navier--Stokes equations and the Keller--Segel system in variable Fourier--Besov spaces
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arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866912106670981120 |
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| author | Vergara-Hermosilla, Gastón Zhao, Jihong |
| author_facet | Vergara-Hermosilla, Gastón Zhao, Jihong |
| contents | In this paper, we study the Cauchy problem of the classical incompressible Navier--Stokes equations and the parabolic-elliptic Keller--Segel system in the framework of the Fourier--Besov spaces with variable regularity and integrability indices. By fully using some basic properties of these variable function spaces, we establish the linear estimates in variable Fourier--Besov spaces for the heat equation. Such estimates are fundamental for solving certain PDE's of parabolic type. As an applications, we prove global well-posedness in variable Fourier--Besov spaces for the 3D classical incompressible Navier--Stokes equations and the 3D parabolic-elliptic Keller--Segel system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_05293 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global well-posedness of the Navier--Stokes equations and the Keller--Segel system in variable Fourier--Besov spaces Vergara-Hermosilla, Gastón Zhao, Jihong Analysis of PDEs 35A01, 35Q30, 46E30, 92C17 In this paper, we study the Cauchy problem of the classical incompressible Navier--Stokes equations and the parabolic-elliptic Keller--Segel system in the framework of the Fourier--Besov spaces with variable regularity and integrability indices. By fully using some basic properties of these variable function spaces, we establish the linear estimates in variable Fourier--Besov spaces for the heat equation. Such estimates are fundamental for solving certain PDE's of parabolic type. As an applications, we prove global well-posedness in variable Fourier--Besov spaces for the 3D classical incompressible Navier--Stokes equations and the 3D parabolic-elliptic Keller--Segel system. |
| title | Global well-posedness of the Navier--Stokes equations and the Keller--Segel system in variable Fourier--Besov spaces |
| topic | Analysis of PDEs 35A01, 35Q30, 46E30, 92C17 |
| url | https://arxiv.org/abs/2410.05293 |