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We consider a set of bipolar Euler-Poisson equations and study two asymptoticlimiting processes. The first is the zero-electron-mass limit, which formallyresults in a non-linear adiabatic electron system. In a second step, we analysethe combined zero-electron-mass and quasi-neutral limits, which together leadto the compressible Euler equations. Using the relative energy method, werigorously justify these limiting processes for weak solutions of thetwo-species Euler-Poisson equations that dissipate energy, as well as forstrong solutions of the limit systems that are bounded away from vacuum. Thisjustification is valid in the regime of initial data for which strong solutionsexist. To deal with the electric potential, in the first case we use elliptictheory, whereas in the second case we employ the theory of Riesz potentials andproperties of the Neumann function.

Zero-electron-mass and quasi-neutral limits for bipolar Euler-Poisson systems