| 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). |
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