We investigate the global existence of strong solutions to a non-isothermal ideal gas model derived from an energy variational approach.We first show the global wellposedness in the Sobolev space H^(2)(R^(3)) for solu...We investigate the global existence of strong solutions to a non-isothermal ideal gas model derived from an energy variational approach.We first show the global wellposedness in the Sobolev space H^(2)(R^(3)) for solutions near equilibrium through iterated energy-type bounds and a continuity argument.We then prove the global well-posedness in the critical Besov space B^(3/2)_(2,1) by showing that the linearized operator is a contraction mapping under the right circumstances.展开更多
Let(X,d,μ) be an RD-space with "dimension" n,namely,a space of homogeneous type in the sense of Coifman and Weiss satisfying a certain reverse doubling condition.Using the Calder'on reproducing formula,...Let(X,d,μ) be an RD-space with "dimension" n,namely,a space of homogeneous type in the sense of Coifman and Weiss satisfying a certain reverse doubling condition.Using the Calder'on reproducing formula,the authors hereby establish boundedness for paraproduct operators from the product of Hardy spaces H p(X) × H q(X) to the Hardy space H r(X),where p,q,r ∈(n/(n + 1),∞) satisfy 1/p + 1/q = 1/r.Certain endpoint estimates are also obtained.In view of the lack of the Fourier transform in this setting,the proofs are based on the derivation of appropriate kernel estimates.展开更多
We introduce a class of tri-linear operators that combine features of the bilinear Hilbert transform and paraproduct. For two instances of these operators, we prove boundedness property in alarge range D ={（p1,p2,p3...We introduce a class of tri-linear operators that combine features of the bilinear Hilbert transform and paraproduct. For two instances of these operators, we prove boundedness property in alarge range D ={（p1,p2,p3）ЕR3：1〈p1,p2〈∞,1/p1＋1/p2〈3/2,1〈p3〈∞}展开更多
In this paper, the LP（Rn）-boundedness of the commutators generalized by BMO（Rn） function and the singular integral operator T with rough kernel Ω∈ L log＋ L（Sn-1）is proved by using the Bony＇s formula for the...In this paper, the LP（Rn）-boundedness of the commutators generalized by BMO（Rn） function and the singular integral operator T with rough kernel Ω∈ L log＋ L（Sn-1）is proved by using the Bony＇s formula for the paraproduct of two functions.展开更多
In this note, we consider the following Navier-Stokes equations （n≥2）: where t≥0,x=（x<sub>1</sub>,…,x<sub>n</sub>）,ρ,density,u=（u<sub>1</sub>,…,u<sub>n</sub>）...In this note, we consider the following Navier-Stokes equations （n≥2）: where t≥0,x=（x<sub>1</sub>,…,x<sub>n</sub>）,ρ,density,u=（u<sub>1</sub>,…,u<sub>n</sub>）,velocity,μ,μ’,coefficient of viscosity,μ】0,μ’+2/3μ≥0,P（ρ）,pressure,P’（ρ）】0,ρ】0,1≤i≤n,is a constant,展开更多
In this paper, the authors give the boundedness of the commutator [b,μΩ,γ] from the homogeneous Sobolev space LP（R^n） to the Lebesgue space L^p（R^n） for 1 〈 p 〈 ∞, where μΩ,γ denotes the Marcinkiewicz int...In this paper, the authors give the boundedness of the commutator [b,μΩ,γ] from the homogeneous Sobolev space LP（R^n） to the Lebesgue space L^p（R^n） for 1 〈 p 〈 ∞, where μΩ,γ denotes the Marcinkiewicz integral with rough hypersingular kernel defined by μΩ,γf（x）=（∫0^∞｜∫｜x-y｜≤tΩ（x-y）/｜x-y｜^n-1f（y）dy｜^2dt/t^3＋2γ）^1/2,with Ω∈L^1（S^n-1）for 0〈γ〈min（n/2,n/p）or Ω∈L（log＋L）^β（S^n-1）for｜1-2/p｜〈β〈1（0〈γ〈n/2）,respectively.展开更多
In this paper, the authors give the boundedness of the commutator of hypersingular integral T γ from the homogeneous Sobolev space Lpγ （Rn） to the Lebesgue space Lp（Rn） for 1
基金partially supported by the Zhejiang Province Science Fund(LY21A010009)partially supported by the National Science Foundation of China(12271487,12171097)partially supported by the National Science Foundation(DMS-2012333,DMS-2108209)。
文摘We investigate the global existence of strong solutions to a non-isothermal ideal gas model derived from an energy variational approach.We first show the global wellposedness in the Sobolev space H^(2)(R^(3)) for solutions near equilibrium through iterated energy-type bounds and a continuity argument.We then prove the global well-posedness in the critical Besov space B^(3/2)_(2,1) by showing that the linearized operator is a contraction mapping under the right circumstances.
基金supported by National Science Foundation of US (Grant No. DMS 0400387)the University of Missouri Research Council (Grant No. URC-07-067)National Natural Science Foundation of China (Grant No.10871025)
文摘Let(X,d,μ) be an RD-space with "dimension" n,namely,a space of homogeneous type in the sense of Coifman and Weiss satisfying a certain reverse doubling condition.Using the Calder'on reproducing formula,the authors hereby establish boundedness for paraproduct operators from the product of Hardy spaces H p(X) × H q(X) to the Hardy space H r(X),where p,q,r ∈(n/(n + 1),∞) satisfy 1/p + 1/q = 1/r.Certain endpoint estimates are also obtained.In view of the lack of the Fourier transform in this setting,the proofs are based on the derivation of appropriate kernel estimates.
文摘We introduce a class of tri-linear operators that combine features of the bilinear Hilbert transform and paraproduct. For two instances of these operators, we prove boundedness property in alarge range D ={（p1,p2,p3）ЕR3：1〈p1,p2〈∞,1/p1＋1/p2〈3/2,1〈p3〈∞}
基金Supported by the Natural Science Foundation of Zhejiang Province(Y6090359, Y6090383)Department of Education of Zhejiang Province(Z200803357)the NNSF of China(10701064)
文摘In this paper, the LP（Rn）-boundedness of the commutators generalized by BMO（Rn） function and the singular integral operator T with rough kernel Ω∈ L log＋ L（Sn-1）is proved by using the Bony＇s formula for the paraproduct of two functions.
基金supported by NNSF of China (Nos.19901021,10371080)Beijing Natural Science Foundation(No. 1013006)+1 种基金Scientific Research Foundation for Returned Overseas Chinese Scholarssupported by the National 973 project (G19990751)
文摘In this paper we consider the commutators of fractional integrals
基金Project supported by the National Natural Science Foundation of China.
文摘In this note, we consider the following Navier-Stokes equations （n≥2）: where t≥0,x=（x<sub>1</sub>,…,x<sub>n</sub>）,ρ,density,u=（u<sub>1</sub>,…,u<sub>n</sub>）,velocity,μ,μ’,coefficient of viscosity,μ】0,μ’+2/3μ≥0,P（ρ）,pressure,P’（ρ）】0,ρ】0,1≤i≤n,is a constant,
基金Supported by National Natural Science Foundation of China （Grant Nos. 10931001, 10901017） and Specialized Research Fund for the Doctoral Program of China （Grant No. 20090003110018）Acknowledgements The authors would like to express their gratitude to the referee for his/her very careful reading and many important valuable comments.
文摘In this paper, the authors give the boundedness of the commutator [b,μΩ,γ] from the homogeneous Sobolev space LP（R^n） to the Lebesgue space L^p（R^n） for 1 〈 p 〈 ∞, where μΩ,γ denotes the Marcinkiewicz integral with rough hypersingular kernel defined by μΩ,γf（x）=（∫0^∞｜∫｜x-y｜≤tΩ（x-y）/｜x-y｜^n-1f（y）dy｜^2dt/t^3＋2γ）^1/2,with Ω∈L^1（S^n-1）for 0〈γ〈min（n/2,n/p）or Ω∈L（log＋L）^β（S^n-1）for｜1-2/p｜〈β〈1（0〈γ〈n/2）,respectively.
基金supported by National Natural Science Foundation of China (Grant No. 10901017)Program for New Century Excellent Talents in University of China (Grant No. NCET-11-0574) +3 种基金the Fundamental Research Funds for the Central Universitiessupported by National Natural Science Foundation of China (Grant No. 10931001)the Research Fund for the Dectoral Program of Higher Education of China (Grant No. 20090003110018)Program for Changjiang Scholars and Innovative Research Team in University of China
文摘In this paper, the authors give the boundedness of the commutator of hypersingular integral T γ from the homogeneous Sobolev space Lpγ （Rn） to the Lebesgue space Lp（Rn） for 1
