Well posedness for pressureless Euler system with a flocking dissipation in Wasserstein space

We prove the well posedness of nonhomogeneous pressureless Euler system in 2-Wasserstein space with the initial mass and energy being finite. Our method is based on a main observation pioneered by Brenier and Grenier that we can recover the solution of the pressureless system from a conservation law with its flux function being determined by the initial density and velocity.