The paper deals with a Cauchy problem for the chemotaxis system with the effect of fluid■where d≥2.It is known that for each∈>0 and all sufficiently small initial data(u_(0),n_(0),c_(0))belongs to certain Fourie...The paper deals with a Cauchy problem for the chemotaxis system with the effect of fluid■where d≥2.It is known that for each∈>0 and all sufficiently small initial data(u_(0),n_(0),c_(0))belongs to certain Fourier space,the problem possesses a unique global solution(u^(∈),n^(∈),c^(∈))in Fourier space.The present work asserts that these solutions stabilize to(u^(∞),n^(∞),c^(∞))as∈^(-1)→0.Moreover,we show that c^(∈)(t)has the initial layer as∈^(-1)→0.As one expects its limit behavior maybe give a new viewlook to understand the system.展开更多
In this paper, by establishing a result concerning the mapping properties for bi（sub）linear operators on Morrey spaces, and the weighted estimates with general weights for the bilinear Fourier multiplier, the author...In this paper, by establishing a result concerning the mapping properties for bi（sub）linear operators on Morrey spaces, and the weighted estimates with general weights for the bilinear Fourier multiplier, the author establishes some results concerning the behavior on the product of Morrey spaces for bilinear Fourier multiplier operator with associated multiplierσ satisfying certain Sobolev regularity.展开更多
The authors establish operator-valued Fourier multiplier theorems on Triebel spaces on R^N, where the required smoothness of the multiplier functions depends on the dimension N and the indices of the Triebel spaces. T...The authors establish operator-valued Fourier multiplier theorems on Triebel spaces on R^N, where the required smoothness of the multiplier functions depends on the dimension N and the indices of the Triebel spaces. This is used to give a sufficient condition of the maximal regularity in the sense of Triebel spaces for vector-valued Cauchy problems with Dirichlet boundary conditions.展开更多
This paper concerns the Cauchy problem of the 3D generalized incompressible magneto-hydrodynamic(GMHD) equations. By using the Fourier localization argument and the Littlewood-Paley theory, we get local well-posedness...This paper concerns the Cauchy problem of the 3D generalized incompressible magneto-hydrodynamic(GMHD) equations. By using the Fourier localization argument and the Littlewood-Paley theory, we get local well-posedness results of the GMHD equations with large initial data(u0, b0) belonging to the critical Fourier-Besov-Morrey spaces FN^1-2α+3/p'+λ/pp,λ,q(R^3) Moreover, stability of global solutions is also discussed.展开更多
This paper introduces a unified operator theory approach to the abstract Fourier analysis over homogeneous spaces of compact groups. Let G be a compact group and H be a closed subgroup of G. Let G/H be the left coset ...This paper introduces a unified operator theory approach to the abstract Fourier analysis over homogeneous spaces of compact groups. Let G be a compact group and H be a closed subgroup of G. Let G/H be the left coset space of H in G and μ be the normalized G-invariant measure on G/H associated to the Weil＇s formula. Then, we present a generalized abstract framework of Fourier analysis for the Hilbert function space L^2 （G / H, μ）.展开更多
Two estimates useful in applications are proved for the Fourier transform in the space L^2(X), where X a symmetric space, as applied to some classes of functions characterized by a generalized modulus of continuity.
基金partial supported by the National Natural Science Foundation of China(Grant Nos.71774073,71988101)Social Scienceof Jiangxi Provincial(Grant No.20YJ02)+1 种基金Natural Science Foundation of Jiangxi Provincial(Grant No.20171BAA208019)partial supported by Jiangxi Provincial Department of Education Science and Technology Research Project(GJJ213110)。
文摘The paper deals with a Cauchy problem for the chemotaxis system with the effect of fluid■where d≥2.It is known that for each∈>0 and all sufficiently small initial data(u_(0),n_(0),c_(0))belongs to certain Fourier space,the problem possesses a unique global solution(u^(∈),n^(∈),c^(∈))in Fourier space.The present work asserts that these solutions stabilize to(u^(∞),n^(∞),c^(∞))as∈^(-1)→0.Moreover,we show that c^(∈)(t)has the initial layer as∈^(-1)→0.As one expects its limit behavior maybe give a new viewlook to understand the system.
文摘In this paper, by establishing a result concerning the mapping properties for bi（sub）linear operators on Morrey spaces, and the weighted estimates with general weights for the bilinear Fourier multiplier, the author establishes some results concerning the behavior on the product of Morrey spaces for bilinear Fourier multiplier operator with associated multiplierσ satisfying certain Sobolev regularity.
文摘The authors establish operator-valued Fourier multiplier theorems on Triebel spaces on R^N, where the required smoothness of the multiplier functions depends on the dimension N and the indices of the Triebel spaces. This is used to give a sufficient condition of the maximal regularity in the sense of Triebel spaces for vector-valued Cauchy problems with Dirichlet boundary conditions.
文摘This paper concerns the Cauchy problem of the 3D generalized incompressible magneto-hydrodynamic(GMHD) equations. By using the Fourier localization argument and the Littlewood-Paley theory, we get local well-posedness results of the GMHD equations with large initial data(u0, b0) belonging to the critical Fourier-Besov-Morrey spaces FN^1-2α+3/p'+λ/pp,λ,q(R^3) Moreover, stability of global solutions is also discussed.
文摘This paper introduces a unified operator theory approach to the abstract Fourier analysis over homogeneous spaces of compact groups. Let G be a compact group and H be a closed subgroup of G. Let G/H be the left coset space of H in G and μ be the normalized G-invariant measure on G/H associated to the Weil＇s formula. Then, we present a generalized abstract framework of Fourier analysis for the Hilbert function space L^2 （G / H, μ）.
文摘Two estimates useful in applications are proved for the Fourier transform in the space L^2(X), where X a symmetric space, as applied to some classes of functions characterized by a generalized modulus of continuity.
