JOURNAL OF DIFFERENTIAL EQUATIONS, v.264, no.8, pp.5360 - 5387
Abstract
We prove the uniqueness of Holder 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.