论文标题
全球规律性到不可压缩的粘弹性系统，并具有一类大型初始数据
Global Regularity to Incompressible Viscoelastic System With a Class of Large Initial Data
论文作者
论文摘要
即使对于全球薄弱的解决方案，全球对于不可压缩的粘弹性流的解决方案的存在一直是一个长期的开放问题。在某些特殊的结构（“ div-curl”条件）下，在\ cite {llzhou，cz}中获得了全局小平滑溶液。但是，到目前为止，具有大量初始数据的结果尚不清楚，并且在本文中进行了研究。我们将提出一个新的结构：锥条件，然后通过一类大型初始数据将全局平滑解决方案推导到3D不可压缩的粘弹性系统。关键是通过将溶液限制为圆锥体来从非线性项的估计值中获得角度数量。
The global existence of solutions to incompressible viscoelastic flows has been a longstanding open problem, even for the global weak solution. Under some special structure ("div-curl" condition) the global small smooth solution was obtained in \cite{llzhou, cz}. However, the result with large initial data remains unknown up to now, and it is studied in this paper. We shall put forward a new structure: the cone-condition and then derive the global smooth solution to 3D incompressible viscoelastic system with a class of large initial data. The key is to gain an angle quantity in the estimate of nonlinear terms by restricting the solution to a cone.
