EXISTENCE OF SMOOTH SOLUTIONS TO COUPLED CHEMOTAXIS-FLUID EQUATIONS
- Authors
- Chae, Myeongju; Kang, Kyungkeun; Lee, Jihoon
- Issue Date
- Jun-2013
- Publisher
- AMER INST MATHEMATICAL SCIENCES-AIMS
- Keywords
- Chemotaxis-fluid equations; Keller-Segel; Navier-Stokes system; global solutions; energy estimates
- Citation
- DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, v.33, no.6, pp 2271 - 2297
- Pages
- 27
- Journal Title
- DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
- Volume
- 33
- Number
- 6
- Start Page
- 2271
- End Page
- 2297
- URI
- https://scholarworks.bwise.kr/cau/handle/2019.sw.cau/57028
- DOI
- 10.3934/dcds.2013.33.2271
- ISSN
- 1078-0947
1553-5231
- Abstract
- We consider a system coupling the parabolic-parabolic Keller-Segel equations to the in- compressible Navier-Stokes equations in spatial dimensions two and three. We establish the local existence of regular solutions and present some blow-up criteria. For two dimensional Navier-Stokes-Keller-Segel equations, regular solutions constructed locally in time are, in reality, extended globally under some assumptions pertinent to experimental observation in [20] on the consumption rate and chemotactic sensitivity. We also show the existence of global weak solutions in spatially three dimensions with rather restrictive consumption rate and chemotactic sensitivity.
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Collections - College of Natural Sciences > Department of Mathematics > 1. Journal Articles
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