The singular convergence of a chemotaxis-fluid system modeling coral fertilization is justified in spatial dimension three.More precisely,it is shown that a solution of parabolic-parabolic type chemotaxis-fluid system...The singular convergence of a chemotaxis-fluid system modeling coral fertilization is justified in spatial dimension three.More precisely,it is shown that a solution of parabolic-parabolic type chemotaxis-fluid system modeling coral fertilization■converges to that of the parabolic-elliptic type chemotaxis-fluid system modeling coral fertiliz ation■in a certain Fourier-Herz space asε^(-1)→0.展开更多
Let A be a symmetric expansive matrix and H^p（R^n） be the anisotropic Hardy space associated with A. For a function m in L∞（R^n）, an appropriately chosen function η in Cc^∞（R^n） and j ∈ Z define mj（ξ） = m...Let A be a symmetric expansive matrix and H^p（R^n） be the anisotropic Hardy space associated with A. For a function m in L∞（R^n）, an appropriately chosen function η in Cc^∞（R^n） and j ∈ Z define mj（ξ） = m（A^jξ）η（ξ）. The authors show that if 0 〈 p 〈 1 and mj belongs to the anisotropic nonhomogeneous Herz space K1^1/P^-1,p（R^n）, then m is a Fourier multiplier from H^p（R^n） to L^V（R^n）. For p = 1, a similar result is obtained if the space K1^0.1（R^n） is replaced by a slightly smaller space K（w）. Moreover, the authors show that if 0 〈 p 〈 1 and if the sequence {（mj）^v} belongs to a certain mixednorm space, depending on p, then m is also a Fourier multiplier from H^p（R^n） to L^v（R^n）.展开更多
In this paper,we study a global zero-relaxation limit problem of the electro-diffusion model arising in electro-hydrodynamics which is the coupled Planck-Nernst-Poisson and Navier-Stokes equations.That is,the paper de...In this paper,we study a global zero-relaxation limit problem of the electro-diffusion model arising in electro-hydrodynamics which is the coupled Planck-Nernst-Poisson and Navier-Stokes equations.That is,the paper deals with a singular limit problem of{u^(∈)_(t)+u^(∈)·▽u^(∈)-Δu^(∈)+▽P^(∈)=Δφ^(∈)▽φ^(∈),in R^(3)×(0,∞),▽·u^(∈)=0,in R^(3)×(0,∞),n^(∈)_(t)+u^(∈)·▽n^(∈)-Δn^(∈)=-▽·(n^(∈)▽φ^(∈)),in R^(3)×(0,∞),ct+u^(∈)·▽c^(∈)-Δc^(∈)=▽·(c^(∈)▽φ^(∈)),in R^(3)×(0,∞),∈^(-1)φ^(∈)_(t)=Δφ^(∈)-n^(∈)+c^(∈),in R^(3)×(0,∞),(u^(∈),n^(∈),c^(∈),φ^(∈))|t=0=(u0,n0,c0,φ0),in R^(3) involving with a positive,large parameter^(∈).The present work show a case that(u^(∈),n^(∈),c^(∈))stabilizes to(u^(∞),n∞,c∞):=(u,n,c)uniformly with respect to the time variable as^(∈)→+∞with respect to the strong topology in a certain Fourier-Herz space.展开更多
This paper is devoted to investigating the existence and uniqueness of mild solution to the 3D incompressible micropolar fluid system in the Fourier–Herz framework. By taking advantage of microlocal analysis and the ...This paper is devoted to investigating the existence and uniqueness of mild solution to the 3D incompressible micropolar fluid system in the Fourier–Herz framework. By taking advantage of microlocal analysis and the mutual effect in the same frequency range of convection term, we give a special initial data(u0,ω0) whose norm of FB1,q^-1(q>2) is arbitrarily small, however, the couple(u0,ω0) produces a solution which is arbitrarily large in FB1,q^-1 after an arbitrarily short time. This implies the system is ill-posed in the sense of "norm inflation" as q>2.展开更多
基金Supported by the NSFC(12161041,12001435 and12071197)the training program for academic and technical leaders of major disciplines in Jiangxi Province(20204BCJL23057)+2 种基金the Natural Science Foundation of Jiangxi Province(20212BAB201008)the Educational Commission Science Programm of Jiangxi Province(GJJ190272)Natural Science Foundation of Shandong Province(ZR2021MA031)。
文摘The singular convergence of a chemotaxis-fluid system modeling coral fertilization is justified in spatial dimension three.More precisely,it is shown that a solution of parabolic-parabolic type chemotaxis-fluid system modeling coral fertilization■converges to that of the parabolic-elliptic type chemotaxis-fluid system modeling coral fertiliz ation■in a certain Fourier-Herz space asε^(-1)→0.
基金Supported by NSP of China (Grant No. 10571015)RFDP of China (Grant No. 20050027025).
文摘Let A be a symmetric expansive matrix and H^p（R^n） be the anisotropic Hardy space associated with A. For a function m in L∞（R^n）, an appropriately chosen function η in Cc^∞（R^n） and j ∈ Z define mj（ξ） = m（A^jξ）η（ξ）. The authors show that if 0 〈 p 〈 1 and mj belongs to the anisotropic nonhomogeneous Herz space K1^1/P^-1,p（R^n）, then m is a Fourier multiplier from H^p（R^n） to L^V（R^n）. For p = 1, a similar result is obtained if the space K1^0.1（R^n） is replaced by a slightly smaller space K（w）. Moreover, the authors show that if 0 〈 p 〈 1 and if the sequence {（mj）^v} belongs to a certain mixednorm space, depending on p, then m is also a Fourier multiplier from H^p（R^n） to L^v（R^n）.
基金partial supported by the National Natural Science Foundation of China (Grant Nos. 12161041, 11801236)Training Program for academic and technical leaders of major disciplines in Jiangxi Province (Grant No.20204BCJL23057)+2 种基金Natural Science Foundation of Jiangxi Province (Grant Nos.20212BAB201008 and 20232BAB201013)partial supported by the National Natural Science Foundation of China (Grant Nos. 12001435, 12361050)College Teachers Innovation Fund Project of Gansu Provincial Education Department (2023A-002)。
文摘In this paper,we study a global zero-relaxation limit problem of the electro-diffusion model arising in electro-hydrodynamics which is the coupled Planck-Nernst-Poisson and Navier-Stokes equations.That is,the paper deals with a singular limit problem of{u^(∈)_(t)+u^(∈)·▽u^(∈)-Δu^(∈)+▽P^(∈)=Δφ^(∈)▽φ^(∈),in R^(3)×(0,∞),▽·u^(∈)=0,in R^(3)×(0,∞),n^(∈)_(t)+u^(∈)·▽n^(∈)-Δn^(∈)=-▽·(n^(∈)▽φ^(∈)),in R^(3)×(0,∞),ct+u^(∈)·▽c^(∈)-Δc^(∈)=▽·(c^(∈)▽φ^(∈)),in R^(3)×(0,∞),∈^(-1)φ^(∈)_(t)=Δφ^(∈)-n^(∈)+c^(∈),in R^(3)×(0,∞),(u^(∈),n^(∈),c^(∈),φ^(∈))|t=0=(u0,n0,c0,φ0),in R^(3) involving with a positive,large parameter^(∈).The present work show a case that(u^(∈),n^(∈),c^(∈))stabilizes to(u^(∞),n∞,c∞):=(u,n,c)uniformly with respect to the time variable as^(∈)→+∞with respect to the strong topology in a certain Fourier-Herz space.
基金supported by the National Natural Science Foundation of China(Grant Nos.11501020,11871087 and 11771423)
文摘This paper is devoted to investigating the existence and uniqueness of mild solution to the 3D incompressible micropolar fluid system in the Fourier–Herz framework. By taking advantage of microlocal analysis and the mutual effect in the same frequency range of convection term, we give a special initial data(u0,ω0) whose norm of FB1,q^-1(q>2) is arbitrarily small, however, the couple(u0,ω0) produces a solution which is arbitrarily large in FB1,q^-1 after an arbitrarily short time. This implies the system is ill-posed in the sense of "norm inflation" as q>2.
