On the existence of local strong solutions to chemotaxis-shallow water system with large data and vacuum. (English) Zbl 1351.35128
Summary: In this paper, motivated by the chemotaxis-Navier-Stokes system arising from mathematical biology [I. Tuval et al., Proc. Natl. Acad. Sci. USA 102, No. 7, 2277–2282 (2005; Zbl 1277.35332)], a modified shallow water type chemotactic model is derived. For large initial data allowing vacuum, the local existence of strong solutions together with the blow-up criterion is established.
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
| 76N10 | Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics |
| 92C17 | Cell movement (chemotaxis, etc.) |
| 35M10 | PDEs of mixed type |
| 35Q30 | Navier-Stokes equations |
| 35D35 | Strong solutions to PDEs |
| 35B45 | A priori estimates in context of PDEs |
| 35B44 | Blow-up in context of PDEs |
Keywords:
strong solution; chemotaxis-fluid interaction; shallow water system; vacuum; A priori estimateCitations:
Zbl 1277.35332References:
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