Special Session 1: Analysis of parabolic models for chemotaxis

Analysis of a Navier-Stokes-Cahn-Hilliard system with unmatched densities and chemotaxis
Andrea Giorgini
Politecnico di Milano
Italy
Co-Author(s):    
Abstract:
We consider the initial-boundary value problem for an incompressible Navier-Stokes-Cahn-Hilliard model with non-constant density and chemotaxis for soluble species proposed by Abels, Garcke and Gr\{u}n in 2012. In this talk I will present recent results concerning the global existence of weak solutions and propagation of regularity. A main feature of this contribution is the lack of the regularization effect given by the logistic source in the equation for the density of the soluble species. This is a joint work with Jingning He (The Hong Kong Polytechnic University) and Hao Wu (Fudan University).