Dissipative measure-valued solutions for the Euler-Poisson equation

We consider pressureless compressible Euler equations driven by nonlocal repulusion-attraction and alignment forces. Our attention is directed to measure-valued solutions, i.e., very weak solutions described by a classical Young measure together with appropriate concentration defects. We investigate the evolution of a relative energy functional to compare a measure-valued solution to a regular solution emanating from the same initial datum. This leads to a weak-strong uniqueness principle.Non UBCUnreviewedAuthor affiliation: University of WarsawFacult