On the fractional chemotaxis Navier-Stokes system in the critical spaces

Joelma Azevedo; Claudio Cuevas; Jarbas Dantas; Clessius Silva

doi:10.3934/dcdsb.2022088

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2023, Volume 28, Issue 1: 538-559. Doi: 10.3934/dcdsb.2022088

This issue Previous Article Asymptotically autonomous dynamics for non-autonomous stochastic

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-Navier-Stokes equation with additive noise Next Article Nonlocal biharmonic evolution equations with Dirichlet and Navier boundary conditions

On the fractional chemotaxis Navier-Stokes system in the critical spaces

1.
Departamento de Matemática, Universidade de Pernambuco, Nazaré da Mata-PE, Brazil
2.
Departamento de Matemática, Universidade Federal de Pernambuco, Recife-PE, Brazil
3.
Departamento de Matemática, Universidade Federal Rural de Pernambuco, Recife-PE, Brazil

^*Corresponding author: Claudio Cuevas
^*Corresponding author: Claudio Cuevas

Received: September 30, 2021

Revised: February 28, 2022

Early access: May 2022

Published: January 2023

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Abstract

We consider the fractional chemotaxis Navier-Stokes equations which are the fractional Keller-Segel model coupled with the Navier-Stokes fluid in the whole space, and prove the existence of global mild solutions with the small critical initial data in Besov-Morrey spaces. Our results enable us to obtain the self-similar solutions provided the initial data are homogeneous functions with small norms and considering the case of chemical attractant without degradation rate. Moreover, we show the asymptotic stability of solutions as the time goes to infinity and obtain a class of asymptotically self-similar ones.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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