  We consider the aggregation equation $\rho_{t}-\nabla\cdot(\rho\nabla
K\ast\rho) =0$ in $\mathbb{R}^{n}$, where the interaction potential $K$
incorporates short-range Newtonian repulsion and long-range power-law
attraction. We study the global well-posedness of solutions and investigate
analytically and numerically the equilibrium solutions. We show that there
exist unique equilibria supported on a ball of $\mathbb{R}^n$. By using the
method of moving planes we prove that such equilibria are radially symmetric
and monotone in the radial coordinate. We perform asymptotic studies for the
limiting cases when the exponent of the power-law attraction approaches
infinity and a Newtonian singularity, respectively. Numerical simulations
suggest that equilibria studied here are global attractors for the dynamics of
the aggregation model.
