SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 1993-2026, January 2021.
We establish existence of solutions in a scale of classes weaker than the finite energy Leray class and stronger than the infinite energy Lemarié-Rieusset class. The new classes are based on the $L^2$ Wiener amalgam spaces. Solutions in the classes closer to the Leray class are shown to satisfy some properties known in the Leray class but not the Lemarié-Rieusset class, namely, eventual regularity and long-time estimates on the growth of the local energy. In this sense, these solutions bridge the gap between Leray's original solutions and Lemarié-Rieusset solutions and help identify scalings at which certain properties may break down.

中文翻译：

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维纳汞合金空间中Navier-Stokes方程的局部能量解

SIAM数学分析杂志，第53卷，第2期，第1993-2026页，2021年1月。
我们建立了比有限能量Leray类弱且比无限能量Lemarié-Rieusset类强的类的解的存在性。新类基于$ L ^ 2 $ Wiener汞合金空间。显示出更接近Leray类的类中的解满足Leray类中已知的某些属性，但不满足Lemarié-Rieusset类中的某些属性，即最终的规律性和对局部能量增长的长期估计。从这个意义上讲，这些解决方案弥合了Leray原始解决方案与Lemarié-Rieusset解决方案之间的鸿沟，并有助于确定某些特性可能会失效的缩放比例。