摘要
This paper is concerned with two aspects of the fractional Navier-Stokes equation. First, we establish the local L^(2)theory of the hypo-dissipative Navier-Stokes system. More precisely, the existence of local-in-time as well as global-in-time local energy weak solutions to the hypo-dissipative Navier-Stokes system is proved.In particular, in order to construct a pressure with an explicit representation, some technical innovations are required due to the lack of known results on the local regularity of the non-local Stokes operator. Secondly, as an important application to the local L^(2)theory, we give a second construction of large self-similar solutions of the hypo-dissipative Navier-Stokes system along with the Leray-Schauder degree theory.
基金
supported by National Natural Science Foundation of China(Grant Nos.11871087 and 11971148)。
