Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 2965-3004 |
| Number of pages | 40 |
| Journal | SIAM Journal on Mathematical Analysis |
| Volume | 49 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 2017 Jan 1 |
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All Science Journal Classification (ASJC) codes
- Analysis
- Computational Mathematics
- Applied Mathematics
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Existence of weak solutions in wasserstein space for a chemotaxis model coupled to fluid equations. / Kang, Kyungkeun; Kim, Hwa Kil.
In: SIAM Journal on Mathematical Analysis, Vol. 49, No. 4, 01.01.2017, p. 2965-3004.Research output: Contribution to journal › Article
TY - JOUR
T1 - Existence of weak solutions in wasserstein space for a chemotaxis model coupled to fluid equations
AU - Kang, Kyungkeun
AU - Kim, Hwa Kil
PY - 2017/1/1
Y1 - 2017/1/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85028621167&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85028621167&partnerID=8YFLogxK
U2 - 10.1137/16M1083232
DO - 10.1137/16M1083232
M3 - Article
AN - SCOPUS:85028621167
VL - 49
SP - 2965
EP - 3004
JO - SIAM Journal on Mathematical Analysis
JF - SIAM Journal on Mathematical Analysis
SN - 0036-1410
IS - 4
ER -