Work

On the Cauchy problem for the fractional Keller–Segel system in variable Lebesgue spaces

Year: 2026

Type: article

Abstract: In this paper, we are mainly concerned with the well-posed problem of the fractional Keller–Segel system in the framework of variable Lebesgue spaces. Based on carefully examining the algebraical structure of the system, we reduced the fractional Keller–Segel system into the generalized nonlinear dissipative equation to overcome the difficulties caused by the boundedness of the Riesz potential in a variable Lebesgue spaces, then by mixing some structural properties of the variable Lebesgue spaces with the optimal decay estimates of the fractional heat kernel, we were able to establish global exisentce with small initial data, and local existence and regularity of solutions for the fractional Keller–Segel system in this functional setting.

Source: Applicable Analysis

DOI: 10.1080/00036811.2026.2695798

Authors: Gastón Vergara-Hermosilla, Jihong Zhao

Institutions: Westlake University, Laboratoire de Mathématiques et Modélisation d'Évry, Baoji University of Arts and Sciences

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Natural Science Foundation of Shaanxi Province, Agencia Nacional de Investigación y Desarrollo

Awards: G2599309521, G6551031688, G7892882979