论文标题
多维压缩欧拉方程中奇点形成的定位
Localization of the formation of singularities in multidimensional compressible Euler equations
论文作者
论文摘要
我们考虑了在许多维度上可压缩欧拉方程的平滑数据的库奇问题，并集中在两种情况下：有限质量和能量和解决方案的解决方案，与非平凡固定状态的紧凑扰动相对应。我们使用溶液在空间中的传播的特征来证明爆炸结果，并根据初始数据在给定空间区域中平滑溶液的密度找到上和下限。为了解决问题，我们引入了一个特殊的整体功能家族，并研究了它们的时间动态。
We consider the Cauchy problem with smooth data for compressible Euler equations in many dimensions and concentrate on two cases: solutions with finite mass and energy and solutions corresponding to a compact perturbation of a nontrivial stationary state. We prove the blowup results using the characteristics of the propagation of the solution in space and find upper and lower bounds for the density of a smooth solution in a given region of space in terms of the initial data. To solve the problems, we introduce a special family of integral functionals and study their temporal dynamics.
