一类三维非粘性可压流体力学方程解的有限传播速度及奇异性

Finite Propagation Speed and Singularityof the Solution for a System of Three-Dimensional Inviscid Compressible Fluid Equations

研究了一类三维非粘性的可压流体力学方程局部光滑解的性质,证明了当方程的初值满足一定条件时,解在有限时间内会形成奇异.讨论了此方程具有有限传播速度,并利用有限传播速度讨论解的奇异性.解的有限传播速度对研究解的奇异性起非常重要的作用.

The properties of local smooth solutions of a system of three dimensional inviscid compressible fluid equations were investigated.It is proved that a singular solution will be generated in the limited time when the initial value of the equations satisfies some conditions.The finite speed of propagation was discussed and used to study the singularity of the solution.The finite speed of propagation of the solution plays a very important role to study the singularity of the solution.