Blowup of Regular Solutions and C 1 Solutions for Free Boundary Problem of Two-fluid Euler-Poisson Equations with a background constant in R n

The compressible two-fluid isentropic Euler-Poisson equations are important models in semiconductor physics and plasmas. In this paper, we consider the characteristic curve to obtain the growth rate of the solutions with free boundary, and successfully give the new blowup results of regular solutions for 1 < γ < 2 or 1 < β < 2 or C 1 solutions for γ ≥ 2 and β ≥ 2 of the radially symmetrical two-fluid Euler-Poisson equations with a background constant Λ in R N (N ≥ 2). By using the integration method and assuming that the appropriate initial functional is sufficiently large, we show the singularity of the solutions to two-fluid Euler-Poisson equations in finite time. Mathematics Subject Classification (2010). 76T10, 35R35, 35B44, 74G40.