In this paper, we establish the local existence of weak solutions with higher regularity of the threedimensional half-space compressible isentropic Navier-Stokes equations with the adiabatic exponent γ > 1 in the ...In this paper, we establish the local existence of weak solutions with higher regularity of the threedimensional half-space compressible isentropic Navier-Stokes equations with the adiabatic exponent γ > 1 in the presence of vacuum. Here we do not need any smallness of the initial data.展开更多
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...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.展开更多
基金supported by National Natural Science Foundation of China (Grant No. 11771300)the Research Foundation for “Kong Que” Talents of Shenzhen+1 种基金supported by National Natural Science Foundation of China (Grant Nos. 11971464, 11688101, 11731007 and 11671412)outh Innovation Promotion Association, Chinese Academy of Sciences
文摘In this paper, we establish the local existence of weak solutions with higher regularity of the threedimensional half-space compressible isentropic Navier-Stokes equations with the adiabatic exponent γ > 1 in the presence of vacuum. Here we do not need any smallness of the initial data.
基金supported by National Natural Science Foundation of China(Grant Nos.11871087 and 11971148)。
文摘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.
