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

Autor:	Vergara-Hermosilla, Gastón, Zhao, Jihong
Rok vydání:	2024
Předmět:	Mathematics - Analysis of PDEs 35A01 35Q30 46E30 92C17
Druh dokumentu:	Working Paper
Popis:	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. Comment: 21 pages. arXiv admin note: text overlap with arXiv:2405.01209
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2410.00060 Zobrazit plný text záznamu View this record from Arxiv