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

We study the global-in-time well-posedness for the pressureless Euler-alignment system with singular communication weights phi(r) = r(-gamma), gamma is an element of(0, d). Here d is an element of 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.

Automated summary

This study investigates the global-in-time well-posedness of the pressureless Euler-alignment system with singular communication weights. A global-in-time bounded solution is constructed using the method of characteristics, and uniqueness is obtained via optimal transport techniques.