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 - <p style="text-align: justify;">This paper is concerned with a fully parabolic Patlak-Keller-Segel-Navier-Stokes system<br/></p><p style="text-align:center"><img src="https://admin.global-sci.org/uploads/ueditor/image/20250603/1748917830643707.png" title="1748917830643707.png" alt="image.png"/></p><p style="text-align: justify;">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<br/></p><p style="text-align:center"><img src="https://admin.global-sci.org/uploads/ueditor/image/20250603/1748917844941955.png" title="1748917844941955.png" alt="image.png" width="137" height="49"/></p><p style="text-align: justify;">then the solution of the above system is global and bounded in time.<br/></p>