Blowup of regular solutions and C¹ solutions for free boundary problem of Euler–Poisson equations with repulsive force in Rⁿ

The compressible Euler–Poisson equations are the fundamental models in semiconductor physics and astrophysics. In this paper, by controlling the growth rate of the solutions with free boundary, we successfully show the new blowup phenomenon of the regular solutions for 1 < γ< 2 and C¹ solutions for γ≥ 2 with radial symmetry of the Euler–Poisson equations with repulsive force in Rⁿ (n≥ 2). By considering the characteristic curve, we obtain a n-dimensional boundary growth result, where n≥ 3 or n= 2. Under the assumption on the large functional of initial data, we use the integration method to establish the singularity of the solutions in finite time. Copyright © 2022 The Author(s), under exclusive licence to Springer.