Let X be a space of homogenous type and ψ： X × [0,∞） → [0,∞） be a growth function such that ψ（·,t） is a Muckenhoupt weight uniformly in t and ψ（x,·） an Orlicz function of uniformly upper ty...Let X be a space of homogenous type and ψ： X × [0,∞） → [0,∞） be a growth function such that ψ（·,t） is a Muckenhoupt weight uniformly in t and ψ（x,·） an Orlicz function of uniformly upper type 1 and lower type p ∈（0,1].In this article,the authors introduce a new Musielak–Orlicz BMO-type space BMOψA（X） associated with the generalized approximation to the identity,give out its basic properties and establish its two equivalent characterizations,respectively,in terms of the spaces BMOψA,max（X） and BMOψA（X）.Moreover,two variants of the John–Nirenberg inequality on BMOψA（X） are obtained.As an application,the authors further prove that the space BMOψΔ1/2（Rn）,associated with the Poisson semigroup of the Laplace operator Δ on Rn,coincides with the space BMOψ（Rn） introduced by Ky.展开更多
We consider a Keller–Segel model coupled to the incompressible Navier–Stokes system in 3-dimensional case.We prove that the system has a unique local solution when(u0,n0,c0)∈Φ_(01)^(1)×Φ_(01)^(2)×Φ_(01...We consider a Keller–Segel model coupled to the incompressible Navier–Stokes system in 3-dimensional case.We prove that the system has a unique local solution when(u0,n0,c0)∈Φ_(01)^(1)×Φ_(01)^(2)×Φ_(01)^(3),where Φ_(01)^(1)×Φ_(01)^(2)×Φ_(01)^(3) is a subspace of bmo^(−1)(R^(3))×B˙_(p,∞)^(−2+3/p) (R^(3))×(B˙_(q,∞)^(3/q) (R^(3))∩L^(∞)(R^(3))).Furthermore,we obtain that the system exists a unique global solution for any small initial data(u0,n0,c0)∈BMO^(−1)(R^(3))×B˙_(p,∞)^(−2+3/p)(R^(3))×(B_(q,∞)^(3/q)(R^(3))∩L^(∞)(R^(3))).For the difference between these spaces and known ones,our results may be regarded as a new existence theorem on the system.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11171027 and 11361020)the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20120003110003)the Fundamental Research Funds for Central Universities of China(Grant Nos.2012LYB26,2012CXQT09 and lzujbky-2014-18)
文摘Let X be a space of homogenous type and ψ： X × [0,∞） → [0,∞） be a growth function such that ψ（·,t） is a Muckenhoupt weight uniformly in t and ψ（x,·） an Orlicz function of uniformly upper type 1 and lower type p ∈（0,1].In this article,the authors introduce a new Musielak–Orlicz BMO-type space BMOψA（X） associated with the generalized approximation to the identity,give out its basic properties and establish its two equivalent characterizations,respectively,in terms of the spaces BMOψA,max（X） and BMOψA（X）.Moreover,two variants of the John–Nirenberg inequality on BMOψA（X） are obtained.As an application,the authors further prove that the space BMOψΔ1/2（Rn）,associated with the Poisson semigroup of the Laplace operator Δ on Rn,coincides with the space BMOψ（Rn） introduced by Ky.
基金Supported by NSFC(Grant Nos.12161041 and 12071197)Training Program for academic and technical leaders of major disciplines in Jiangxi Province(Grant No.20204BCJL23057)Natural Science Foundation of Jiangxi Province(Grant No.20212BAB201008)。
文摘We consider a Keller–Segel model coupled to the incompressible Navier–Stokes system in 3-dimensional case.We prove that the system has a unique local solution when(u0,n0,c0)∈Φ_(01)^(1)×Φ_(01)^(2)×Φ_(01)^(3),where Φ_(01)^(1)×Φ_(01)^(2)×Φ_(01)^(3) is a subspace of bmo^(−1)(R^(3))×B˙_(p,∞)^(−2+3/p) (R^(3))×(B˙_(q,∞)^(3/q) (R^(3))∩L^(∞)(R^(3))).Furthermore,we obtain that the system exists a unique global solution for any small initial data(u0,n0,c0)∈BMO^(−1)(R^(3))×B˙_(p,∞)^(−2+3/p)(R^(3))×(B_(q,∞)^(3/q)(R^(3))∩L^(∞)(R^(3))).For the difference between these spaces and known ones,our results may be regarded as a new existence theorem on the system.
