Local well‐posedness of classical solutions for the kinetic self‐organized model of Cucker–Smale type

Abstract

We study in this paper the local well‐posedness of classical solutions to the Cauchy problem for a kinetic self‐organized model of Cucker–Smale type for collective motions, which includes two cases of velocity alignment mechanisms: normalized and nonnormalized reorientation cases. The main concern is the a priori estimates for both cases. Our treatments rely on two key ingredients: One point is to deal with the possible singularity and high nonlinearity arising from the normalized/nonnormalized mean velocity, and the other is to control the growth with respect to the microscopic velocity variable in the whole space by employing weighted estimates.