论文标题
关于不可压缩的Navier-Stokes方程的弱解决方案的独特性
On uniqueness of weak solutions of the incompressible Navier-Stokes equations
论文作者
论文摘要
在本文中，研究了有关3维情况下不可压缩的Navier-Stokes方程弱解的唯一性的问题。在这里，调查是通过使用另一种方法进行的。在具有一定的平稳性的空间中，给定功能证明了对考虑问题的速度的唯一性。此外，这些空间在各自的功能空间中是密集的，在这些空间下，这些空间被证明存在薄弱的解决方案。此外，研究了与主要问题相关的辅助问题的弱解的可溶性和独特性，还证明了一个有条件的结果。
In this article the question on uniqueness of weak solution of the incompressible Navier-Stokes Equations in the 3-dimensional case is studied. Here the investigation is carried out with use of another approach. The uniqueness of velocity for the considered problem is proved for given functions from spaces that posseses some smoothness. Moreover, these spaces are dense in respective spaces of functions, under which were proved existence of the weak solutions. In addition here the solvability and uniqueness of the weak solutions of auxiliary problems associated with the main problem is investigated, and also one conditional result on uniqueness is proved.
