摘要本文考虑一文空间中理想气体的等熵相对论欧拉方程组在初值受到挤压和流体向外流出时经典解的奇性形成问题. 基于数学方面的证明和数学方法的应用,我们采用新的状态方程,本文中我们的状态方程为 . 我们的证明主要基于Thomas C.Sideris在文[2]中的方法. 通过设定合适的与解有关的泛函,我们证明该泛函满足微分不等式,而且该微分不等式的光滑解会发生爆破.因而证明了我们该问题的结论.20135
关键字:非相对论 欧拉方程 解的爆破
Abstrct:
In this paper, we will shows that the isentropic relativistic Euler equations will develop singularities if, on average, it is slightly compressed and out-going near the wave front.
Our proof is mainly based on the Sideris’ method in [2]. By assumping proper functionals coming from the solutions, we obtain a differential inequalities, which solutions will blow up in finite time. Thus, we obtain the result.
Keywords:theory of relativity Euler equation Blow up of solution