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

Fuente: arXiv
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Autores principales: Vergara-Hermosilla, Gastón, Zhao, Jihong
Formato: Preprint
Publicado: 2024
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author Vergara-Hermosilla, Gastón
Zhao, Jihong
author_facet Vergara-Hermosilla, Gastón
Zhao, Jihong
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2410_00060
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Global well-posedness of the fractional dissipative system in the framework of variable Fourier--Besov spaces
Vergara-Hermosilla, Gastón
Zhao, Jihong
Analysis of PDEs
35A01, 35Q30, 46E30, 92C17
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.
title Global well-posedness of the fractional dissipative system in the framework of variable Fourier--Besov spaces
topic Analysis of PDEs
35A01, 35Q30, 46E30, 92C17
url https://arxiv.org/abs/2410.00060