We prove the uniqueness of Hölder continuous weak solutions via duality argument and vanishing viscosity method for the Keller–Segel system of porous medium type equations coupled to the Stokes system in dimensions three. An important step is the estimate of the Green function of parabolic equations with lower order terms of variable coefficients, which seems to be of independent interest.
Bibliographical noteFunding Information:
H. Bae was supported by NRF-2015R1D1A1A01058892.
K. Kang was supported by NRF-2017R1A2B4006484 and NRF-20151009350.
S. Kim was supported by NRF-20151009350.
© 2018 Elsevier Inc.
All Science Journal Classification (ASJC) codes
- Applied Mathematics