Volume 4, Issue 2
A Note on the Global Existence in a Fully Parabolic Patlak-Keller-Segel-Navier-Stokes System

Pan Zheng

Commun. Math. Anal. Appl., 4 (2025), pp. 179-201.

Published online: 2025-06

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  • Abstract

This paper is concerned with a fully parabolic Patlak-Keller-Segel-Navier-Stokes system

image.png

where $Ω ⊂\mathbb{R}^2$ is a smoothly bounded domain and the parameter $χ$ is positive. The main aim of this note is to show that if

image.png

then the solution of the above system is global and bounded in time.

  • AMS Subject Headings

35B35, 35B40, 35B45, 35K55

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COPYRIGHT: © Global Science Press

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@Article{CMAA-4-179, author = {Zheng , Pan}, title = {A Note on the Global Existence in a Fully Parabolic Patlak-Keller-Segel-Navier-Stokes System}, journal = {Communications in Mathematical Analysis and Applications}, year = {2025}, volume = {4}, number = {2}, pages = {179--201}, abstract = {

This paper is concerned with a fully parabolic Patlak-Keller-Segel-Navier-Stokes system

image.png

where $Ω ⊂\mathbb{R}^2$ is a smoothly bounded domain and the parameter $χ$ is positive. The main aim of this note is to show that if

image.png

then the solution of the above system is global and bounded in time.

}, issn = {2790-1939}, doi = {https://doi.org/10.4208/cmaa.2025-0002}, url = {http://global-sci.org/intro/article_detail/cmaa/24121.html} }
TY - JOUR T1 - A Note on the Global Existence in a Fully Parabolic Patlak-Keller-Segel-Navier-Stokes System AU - Zheng , Pan JO - Communications in Mathematical Analysis and Applications VL - 2 SP - 179 EP - 201 PY - 2025 DA - 2025/06 SN - 4 DO - http://doi.org/10.4208/cmaa.2025-0002 UR - https://global-sci.org/intro/article_detail/cmaa/24121.html KW - Global existence, boundedness, Patlak-Keller-Segel-Navier-Stokes. AB -

This paper is concerned with a fully parabolic Patlak-Keller-Segel-Navier-Stokes system

image.png

where $Ω ⊂\mathbb{R}^2$ is a smoothly bounded domain and the parameter $χ$ is positive. The main aim of this note is to show that if

image.png

then the solution of the above system is global and bounded in time.

Zheng , Pan. (2025). A Note on the Global Existence in a Fully Parabolic Patlak-Keller-Segel-Navier-Stokes System. Communications in Mathematical Analysis and Applications. 4 (2). 179-201. doi:10.4208/cmaa.2025-0002
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