Blowup for regular solutions and C1 solutions of Euler equations in RN with a free boundary

The compressible Euler equations are fundamental models in the study of fluids, plasmas, condensed matter and atmospheric dynamics. In this paper, we analyze the blowup phenomena of the weakened regular solutions (ρ,u→) and the C1 solutions for γ≥2 of the Euler equations in RN in an initial bounded region Ω(0). If maxx→0∈∂Ω̄(0)∑Ni=1ui2(0,x→0)0 is the total mass, then the corresponding solutions blow up in finite time. Our blowup development for the free boundary value problem partially complements the result for the fixed boundary problem (Makino et al. 1986).