Shock Development in Spherical Symmetry
Shock Development in Spherical Symmetry
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DOI：
10.1007/s40818-016-0009-1
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发表时间：
2015-01
期刊：
影响因子：
2.8
通讯作者：
D. Christodoulou;André Lisibach
中科院分区：
文献类型：
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作者：
D. Christodoulou;André Lisibach
D.Christodoulou在[2]中解决了三维空间中激波形成的一般问题。在这项工作中，还提供了初始数据的最大发展的完整描述。该描述设置了在解决方案不再是规则的点之后继续解决方案的问题。这个问题叫做冲击发展问题。它属于自由边界问题的范畴，但由于解在爆破面处的行为，具有奇异的初值。在正压流体为球对称的情况下，本工作给出了这一问题的解决方案。用光滑函数的形式完整地描述了与激波发展有关的奇点。
The general problem of shock formation in three space dimensions was solved by D. Christodoulou in [2]. In this work also a complete description of the maximal development of the initial data is provided. This description sets up the problem of continuing the solution beyond the point where the solution ceases to be regular. This problem is called the shock development problem. It belongs to the category of free boundary problems but in addition has singular initial data because of the behavior of the solution at the blowup surface. The present work delivers the solution to this problem in the case of spherical symmetry for a barotropic fluid. A complete description of the singularities associated to the development of shocks in terms of smooth functions is given.