On the existence of global solutions for the 3D chemorepulsion system
| Autor: | Cieślak, Tomasz, Fuest, Mario, Hajduk, Karol, Sierżęga, Mikołaj |
|---|---|
| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.4171/zaa/1747 |
| Popis: | In this paper, we give sufficient conditions for global-in-time existence of classical solutions for the fully parabolic chemorepulsion system posed on a convex, bounded three-dimensional domain. Our main result establishes global-in-time existence of regular nonnegative solutions provided that $\nabla\sqrt{u} \in L^4(0, T; L^2(\Omega))$. Our method is related to the Bakry--\'Emery calculation and appears to be new in this context. Comment: 14 pages; incorporated referee comments and added alternative proof |
| Databáze: | arXiv |
| Externí odkaz: |
|