Global well-posedness for the Euler-alignment system with singular communication weights in multi-dimensions

Abstract

We study the global-in-time well-posedness for the pressureless Euler-alignment system with singular communication weights ϕ(r)=r−γ, γ∈(0,d). Here d∈N denotes the dimension. Under the assumptions that the initial density has a compact support and the initial velocity is sufficiently small, we construct a global-in-time bounded solution by means of the method of characteristics. The uniqueness is also obtained via optimal transport techniques.