On the analytical aspects of inertial particle motion

In their seminal 1983 paper, M. Maxey and J. Riley introduced an equation for the motion of a sphere through fluid. Since this features Basset history integral, popularity has broadened use certain form fractional differential to study inertial particle motion. we give comprehensive theoretical analysis Maxey-Riley equation. particular, build on previous local in time existence uniqueness results prove that solutions are global time. doing so, also notion maximal solution extends We furthermore conditions under which differentiable at initial By considering derivative with respect conditions, perform sensitivity demonstrate two trajectories can not meet, as well provide control growth distance between pair particles. The properties here equations possessed, mutatis mutandis, by broader class similar form.