论文标题
Wiener Amalgam空间中Navier-Stokes方程的本地能源解决方案
Local energy solutions to the Navier-Stokes equations in Wiener amalgam spaces
论文作者
论文摘要
我们以比有限能量leray类弱的类别中建立解决方案的存在，并且比无限的能量lemarié-rieusset类更强。新课程基于$ l^2 $ wiener amalgam空间。显示出更接近Leray类的班级的解决方案可满足Leray类中已知的某些特性，但不能满足Lemarié-Rieusset类，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的原始解决方案与Lemarié-Rieusset的解决方案之间的差距，并有助于确定某些属性可能分解的尺度。
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's solutions and help identify scalings at which certain properties may break down.
