论文标题
Navier-Stokes方程的离散自相似解决方案的空间衰减
Spatial decay of discretely self-similar solutions to the Navier-Stokes equations
论文作者
论文摘要
已知向前的自我相似和自由相似的弱解，已知在全球范围内存在大型自相似和离散自相似的初始数据，并且已知在时空抛物面之外是规律的。在本文中，我们为在规律性区域中的这种解决方案建立了空间衰减率，前提是初始数据在本地临界规律性远离原点。特别是，我们（1）降低了获得流量非线性衰减率所需的数据的规律性，与现有文献相比，（2）建立新的衰减速率，而没有对数的数据进行对数的校正，（3）为解决方案提供了新的衰减率，并提供了新的衰减率，并且为我们的衰减率提供了快速的范围，（4）的范围，（4），（4）的范围，（4）and（4），（4）的范围（4），（4）ny nourtiant in n of（4），（4）ny nourtiant n offormant nof and（4）（4）（4）当地能源解决方案可以与原点分开。
Forward self-similar and discretely self-similar weak solutions of the Navier-Stokes equations are known to exist globally in time for large self-similar and discretely self-similar initial data and are known to be regular outside of a space-time paraboloid. In this paper, we establish spatial decay rates for such solutions which hold in the region of regularity provided the initial data has locally sub-critical regularity away from the origin. In particular, we (1) lower the Hölder regularity of the data required to obtain an optimal decay rate for the nonlinear part of the flow compared to the existing literature, (2) establish new decay rates without logarithmic corrections for some smooth data, (3) provide new decay rates for solutions with rough data, and, as an application of our decay rates, (4) provide new upper bounds on how rapidly potentially {non-unique}, scaling invariant local energy solutions can separate away from the origin.
