Global well-posedness of the fractional dissipative system in the framework of variable Fourier--Besov spaces

2024/09/29 by Vergara-Hermosilla, Gastón, Zhao, Jihong
#35A01 #35Q30 #46E30 #92C17 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2410.00060

Abstract

In this paper, we are concerned with the well-posed issues of the fractional dissipative 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 fractional heat equation. Such estimates are fundamental for solving certain dissipative PDE's of fractional type. As an applications, we prove global well-posedness in variable Fourier--Besov spaces for the 3D generalized incompressible Navier--Stokes equations and the 3D fractional Keller--Segel system.

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