三维非线性阻尼项的欧拉方程初值问题经典解的爆破

摘要

研究三维带非线性阻尼项的等熵欧拉方程，在假设某些初始数据较大的条件下，研究其初值问题经典解的爆破。在其局部解具有有限传播速度的基础上，通过构造适当的泛函，用泛函方法得到了其经典解在有限时间内必定发生爆破的结论。%The Cauehy problem for the 3-dimensional isentropic Euler equations with nonlinear damping is investigated in this paper, the local solutions for Cauchy problem is obtained and have limited speed by utilizing the theory of the Cauchy problem for quasilinear symmetric hyperbolic systems, furthermore, by functional methods, the classical solutions is proved to be blowed up in finite time provided the some initial data is sufficiently large.