  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.
