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arXiv · 2410.05293

Global well-posedness of the Navier--Stokes equations and the Keller--Segel system in variable Fourier--Besov spaces

Gastón Vergara-Hermosilla·Jihong Zhao
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Abstract

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.

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Gastón Vergara-Hermosilla, Jihong Zhao. 2024-10-03. Global well-posedness of the Navier--Stokes equations and the Keller--Segel system in variable Fourier--Besov spaces. https://arxiv.org/abs/2410.05293

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