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

2024/10/03 by Gastón Vergara-Hermosilla, Jihong Zhao, Vergara-Hermosilla, Gastón +1
Economics, Econometrics and Finance · Mathematics · #35A01 #35Q30 #46E30 #92C17 #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth #Stochastic processes and financial applications #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2410.05293

openalex publication_date 2024/10/03 · openalex created_date 2024/10/10 · openalex updated_date 2026/07/28

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.

Related

• Global well-posedness of the fractional dissipative system in the framework of variable Fourier--Besov spaces
• Global well-posedness for the Navier-Stokes system in new critical mixed-norm Besov spaces
• Besov-weak-Herz spaces and global solutions for Navier-Stokes equations
• Global well-posedness for the Keller--Segel--Navier--Stokes system with nonlinear boundary conditions
• Sharp well-posedness and ill-posedness in Fourier-Besov spaces for the viscous primitive equations of geophysics