粘性可压缩反应气体的爆破

Blow-up of Viscous Compressible Reacting Gas

在初始密度有紧支集且其他初值满足适当条件下,通过利用物理量之间特殊的泛函关系并结合各种不等式,证明了粘性可压缩反应气体模型的光滑解将在有限时间内爆破.特别地,得到了初始密度的紧支集大小与解存在时间之间的关系.

In this paper,we prove the smooth solution of viscous compressible reactive gas model will blow-up in a finite time by using the special functional relationships between physical quantities and combining various inequalities under the condition that the initial density has compact support and the other initial values satisfy proper conditions.In particular,we obtain the relationship between the size of the compact support of initial density and the existence time.