Weak–strong uniqueness and quasi-neutral limit for Euler–Poisson equations

In this paper, we investigate the weak–strong uniqueness and quasi-neutral limit of 3D modified Euler–Poisson equations. Focusing on a weak solution called the dissipative measure-valued solution as the object of study, the global existence is established based on an energy admissibility criterion and by means of relative energy method it is shown that the weak solution and the strong solution, emanating from the same initial data, coincide as long as the latter exists. Moreover, it is proved that the weak solutions of the modified Euler–Poisson equations converge to the smooth solutions of the compressible Euler equations as Debye length tends to zero.