This paper is concerned with a system that can be used to model the diffusion-advection of myosin molecules, which change direction by a certain angle when binding to actin gel. More precisely, we shall consider the parabolic-elliptic Keller-Segel system with rotation Formula: see text; Formula: see text in smoothly bounded planar domains, where Formula: see text is a matrix attaining value in Formula: see text as Formula: see text with Formula: see text. We shall investigate the system accompanied by boundary conditions of no-flux type for Formula: see text and of Dirichlet type for Formula: see text. It is shown that the associated initial-boundary value problem possesses a critical value of the initial mass Formula: see text to distinguish global existence and finite-time blow-up. Furthermore, we study the blowup mechanism, and prove that the number of blowup points is finite and does not exceed Formula: see text. Our results present a precise characterization of the effect of rotational trajectory on the properties of Keller-Segel system in the form of rotational angle.
Wang et al. (Fri,) studied this question.