The aggregation equation with Newtonian potential

TL;DR

This paper studies the aggregation equation with Newtonian potential, establishing well-posedness, decay properties, and the convergence of viscous solutions to inviscid ones as viscosity diminishes.

Contribution

It introduces a generalized form of the aggregation equation with Newtonian potential, providing new results on well-posedness, decay, and viscous-inviscid convergence.

Findings

Proved well-posedness of the generalized aggregation equations.

Established spatial decay properties of viscous solutions.

Showed convergence of viscous solutions to inviscid solutions as viscosity approaches zero.

Abstract

The viscous and inviscid aggregation equation with Newtonian potential models a number of different physical systems, and has close analogs in 2D incompressible fluid mechanics. We consider a slight generalization of these equations in the whole space, establishing well-posedness and spatial decay of the viscous equations, and obtaining the convergence of viscous solutions to the inviscid solution as the viscosity goes to zero.