Journal
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS
Volume 39, Issue 7, Pages 1205-1235Publisher
TAYLOR & FRANCIS INC
DOI: 10.1080/03605302.2013.852224
Keywords
Blow-up criteria; Decay estimates; Keller-Segel; Navier-Stokes
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Funding
- Chung-Ang University Research Grants
- [NRF-2011-0028951]
- [NRF-2012R1A1A2001373]
- [NRF-2011-0006697]
- National Research Foundation of Korea [2011-0028951, 2012R1A1A2001373, 2011-0006697] Funding Source: Korea Institute of Science & Technology Information (KISTI), National Science & Technology Information Service (NTIS)
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We consider a Keller-Segel model coupled to the incompressible Navier-Stokes equations in spatial dimensions two and three. We establish the local existence of regular solutions and present some blow-up criteria for both cases that equations of oxygen concentration is of parabolic or hyperbolic type. We also prove that solutions exist globally in time and upper bounds of temporal decays are obtained under the some smallness conditions of initial data.
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