期刊
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
卷 33, 期 6, 页码 2271-2297出版社
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/dcds.2013.33.2271
关键词
Chemotaxis-fluid equations; Keller-Segel; Navier-Stokes system; global solutions; energy estimates
资金
- National Research Foundation of Korea [NRF-2011-0028951, NRF-2009-0088692, NRF-2011-0006697]
- [KRF-2008-331-C00024]
- National Research Foundation of Korea [2011-0028951, 2009-0088692, 2011-0006697] Funding Source: Korea Institute of Science & Technology Information (KISTI), National Science & Technology Information Service (NTIS)
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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