Open AccessExistence of generalized solutions for Keller-Segel-Navier-Stokes equations with degradation in dimension three
Author(s) -
Kyungkeun Kang,
Dongkwang Kim
Publication year - 2021
Publication title -
mathematics in engineering
Language(s) - English
Resource type - Journals
ISSN - 2640-3501
DOI - 10.3934/mine.2022041
Subject(s) - dimension (graph theory) , mathematics , convergence (economics) , quadratic equation , type (biology) , degradation (telecommunications) , construct (python library) , zero (linguistics) , power (physics) , mathematical analysis , pure mathematics , physics , computer science , thermodynamics , geometry , economics , ecology , telecommunications , linguistics , philosophy , biology , programming language , economic growth
We construct generalized solutions for the Keller-Segel system with a degradation source coupled to Navier Stokes equations in three dimensions, in case that the power of degradation is smaller than quadratic. Furthermore, if the logistic type source is purely damping with no growing effect, we prove that solutions converge to zero in some norms and provide upper bounds of convergence rates in time.