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Enhanced dissipation and blow-up suppression for the three dimensional Keller-Segel equation with the plane Couette-Poiseuille flow.
- Source :
-
Journal of Differential Equations . Sep2024, Vol. 403, p368-405. 38p. - Publication Year :
- 2024
-
Abstract
- In this paper, we consider the Cauchy problem for the three dimensional parabolic-elliptic Keller-Segel equation with the large plane Couette-Poiseuille flow. Without advection, there exist solution with arbitrarily mass which blow up in finite time. Firstly, we introduce three dimensional plane Couette-Poiseuille flow and study the enhanced dissipation effect of such flows by resolvent estimate method. Next, we show that the enhanced dissipation effect of such flows can suppress blow-up of solution to three dimensional parabolic-elliptic Keller-Segel equation and establish global classical solution with large initial data. [ABSTRACT FROM AUTHOR]
- Subjects :
- *CAUCHY problem
*EQUATIONS
*ADVECTION
Subjects
Details
- Language :
- English
- ISSN :
- 00220396
- Volume :
- 403
- Database :
- Academic Search Index
- Journal :
- Journal of Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- 177750270
- Full Text :
- https://doi.org/10.1016/j.jde.2024.05.026