论文标题
估计Navier-Stokes流量的非唯一性和短期渐近扩展
Estimation of non-uniqueness and short-time asymptotic expansions for Navier-Stokes flows
论文作者
论文摘要
有大量证据表明，自然能量空间中未遭受的3D Navier-Stokes方程的解决方案并非唯一。假设是这种情况，那么量化非唯一性的演变是重要的。在本文中，我们提供了一个代数估计，以在两个可能的非唯一解决方案可以在紧凑的空间区域分开，在该空间区域中，初始数据具有亚临界规则性。在这个紧凑的区域之外，仅假定数据位于较大的弱弱Lebesgue空间中，并且可能很大。为了建立这种分离率，我们开发了一个新的空间局部，短期渐近扩张，这具有独立的兴趣。
There is considerable evidence that solutions to the non-forced 3D Navier-Stokes equations in the natural energy space are not unique. Assuming this is the case, it becomes important to quantify how non-uniqueness evolves. In this paper we provide an algebraic estimate for how rapidly two possibly non-unique solutions can separate over a compact spatial region in which the initial data has sub-critical regularity. Outside of this compact region, the data is only assumed to be in the scaling critical weak Lebesgue space and can be large. In order to establish this separation rate, we develop a new spatially local, short-time asymptotic expansion which is of independent interest.
