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Electronic Journal of Qualitative Theory of Differential Equations
Article . 2021 . Peer-reviewed
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Existence of global solutions to chemotaxis fluid system with logistic source

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 2021 English Publisher:University of SzegedJournal:Electronic Journal of Qualitative Theory of Differential Equations (eissn: 1417-3875, Copyright policy )
Authors: Hattori, Harumi; Lagha, Aesha;

doi: 10.14232/ejqtde.2021.1.53

Existence of global solutions to chemotaxis fluid system with logistic source

Abstract

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.

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Keywords

chemotaxis system, QA Mathematics / matematika, fourier transform, a priori estimates, time-decay rates, QA1-939, energy method, Mathematics

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
1
Average
Average
Average
gold
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