Global existence and asymptotic stability for the Toner-Tu model of flocking

Abstract: This paper deals with the Toner-Tu (TT) model, which is a hydrodynamic model describing the collective motion of numerous self-propelled agents. We analytically study the global-in-time well-posedness of the TT model near the steady-state solution in the ordered phase. We also show the large-time behavior of solutions showing that the steady-state solution is polynomially stable in a Sobolev space in the sense that solutions that are initially close to that steady state converge to that at least polynomially fast as time tends to infinity. Moreover, we investigate the variant of the TT model which describes the dynamics of the actin filament.