We consider a coupled system of Keller-Segel-type equations and the incompressible Navier-Stokes equations in spatial dimension two and three. We first establish the existence of a weak solution of a Fokker-Plank equation in the Wasserstein space under the assumption that initial mass is integrable and has finite entropy. As a result, we construct solutions of Keller-Segel-Navier-Stokes equations such that the density of biological organism belongs to the absolutely continuous curves in the Wasserstein space, in the case that its initial mass is assumed to be bounded and integrable.
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∗Received by the editors July 5, 2016; accepted for publication (in revised form) May 2, 2017; published electronically August 3, 2017. http://www.siam.org/journals/sima/49-4/M108323.html Funding: The work of the first author was supported by NRF-2014R1A2A1A11051161 and NRF-20151009350. The work of the second author was supported by NRF-2015R1D1A1A01056696. †Department of Mathematics, Yonsei University, Seoul 120-749, Republic of Korea (kkang@yonsei. ac.kr). ‡School of Mathematics, Korea Institute for Advanced Study, Seoul 02455, Republic of Korea (firstname.lastname@example.org).
© 2017 Society for Industrial and Applied Mathematics.
All Science Journal Classification (ASJC) codes
- Computational Mathematics
- Applied Mathematics