Existence of global solutions to chemotaxis fluid system with logistic source. (English) Zbl 07444210

Hattori, Harumi; Lagha, Aesha

Electron. J. Qual. Theory Differ. Equ. 2021, Paper No. 53, 27 p. (2021).

Summary: We establish the existence of global solutions and \(L^q\) time-decay of a three dimensional chemotaxis system with chemoattractant and repellent. We show the existence of global solutions by the energy method. We also study \(L^q\) time-decay for the linear homogeneous system by using Fourier transform and finding Green’s matrix. Then, we find \(L^q\) time-decay for the nonlinear system using solution representation by Duhamel’s principle and time-weighted estimate.

MSC:

35Q31	Euler equations
35Q35	PDEs in connection with fluid mechanics
35Q92	PDEs in connection with biology, chemistry and other natural sciences
76N10	Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics

Keywords:

chemotaxis system; energy method; a priori estimates; Fourier transform; time-decay rates