扩展晶体PDE
Extended Crystal PDE's
摘要：
在本文中，我们表明，PDE的和晶体群之间有一个不可预见的关系。事实上，我们证明，积分bordism群的偏微分方程的可以被认为是扩大的结晶子群。在这方面，我们可以把PDE看作{ \em扩展晶体}。然后得到了一个代数拓扑阻塞（{ \em crystalobstruction}），它刻画了光滑边值问题整体光滑解的存在性.给出了这一新理论在Ricci流方程和Navier-斯托克斯方程中的应用，解决了一些著名的基本问题。这些结果也被推广到奇异偏微分方程，引入了（{ \em extended crystal singular PDE's}）。应用奇异MHD-PDE的，给出了我们以前的一些结果，这样的方程，并显示存在（有限次稳定光滑）的整体解决方案，通过临界核能生产区。
英文摘要：
In this paper we show that between PDE's and crystallographic groups there is an unforeseen relation. In fact we prove that integral bordism groups of PDE's can be considered extensions of crystallographic subgroups. In this respect we can consider PDE's as {\em extended crystals}. Then an algebraic-topological obstruction ({\em crystal obstruction}), characterizing existence of global smooth solutions for smooth boundary value problems, is obtained. Applications of this new theory to the Ricci-flow equation and Navier-Stokes equation are given that solve some well-known fundamental problems. These results, are also extended to singular PDE's, introducing ({\em extended crystal singular PDE's}). An application to singular MHD-PDE's, is given following some our previous results on such equations, and showing existence of (finite times stable smooth) global solutions crossing critical nuclear energy production zone.
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