3维带粘性Boussinesq方程弱解的一个正则性准则

考虑3维带粘性Boussinesq方程的一组弱解,当解u满足u∈L2(0,T;BMO(R3)),且iu∈L1(0,T;BMO(R3)),i=1,2,3时,该弱解得到一定的正则性.     

非齐次分数阶多孔介质方程的弱解

本文主要讨论了一类具有外力项的分数阶多孔介质方程的弱解存在性: 〖JB({〗〖HL(1:1,Z〗〖SX(〗u〖〗t〖SX)〗+(－Δ)σ/2um=F(u),x∈ R N,t>0,u〖JB((〗x,0〖JB))〗=f(x),x∈ R Ν.〖HL)〗〖JB)〗 其中f∈L1( R N)∩L∞( R N),m>0 和0<σ<2,证明了如果F是一个Lipschitz连续函数,那么此问题存在一个弱解.     

三维Magneto-Hydrodynamics方程关于压强的正则准则

通过Navier-Stokes方程以及利用光滑解的先验估计方法,来探讨三维MHD方程的压强在Besov空间B·r!,!(R3)中的弱解正则准则.证明了当压强π(t)满足:π(t)∈L22+r(0,T;B·r!,!(R3)),-1≤r≤1此条件时,则三维MHD方程的一组弱解(v(x,t),b(x,t))在(0,T]上是正则解.     

Navier-Stokes-Poisson方程的弱解关于区域的连续依赖性

研究了可压等熵Navier-Stokes-Poisson方程的弱解与空间区域的关系.证明了有界区域Ωn(R3)上的弱解收敛到有界区域Ω上的弱解.利用空间区域的性质,可以得到一般非光滑有界的非空区域上弱解的存在性.     

一类经典的Boussinesq系统解的若干问题研究

[目的]研究Boussinesq系统弱解的存在唯一性以及强解的爆破准则.[方法]通过拟抛正规化方法建立Boussinesq系统在Sobolev空间Hs(R)×Hs-1 (R)(s≥1)中弱解的存在和唯一性,利用能量估计、输运方程理论等方法得到系统强解精确的爆破准则.[结果]首先得到了Boussinesq系统在Sobol...     

一个新的三维Navier-Stokes方程的正则性准则

在R3中考虑了Navier-Stokes方程Leary-Hopf弱解的正则性准则问题.通过能量估计的方法,得到了一个新的估计量.即证明如果形变张量的一行(列)满足:σ3j∈Lp(0,T;Lq(R3)),2/p+3/q=2,3/2相似文献   

定重特征线性偏微分算子的局部可解性

对于主型线性偏微分算子,L.Nirenberg,F.Treves R.Beals,C.Feffeman证明了局部存在弱解的充分必要条件,该条件只对算子的主部附加限制,对于非主型算子,即主部具实重特征时,须对低阶项附加限制才能保证解的存在。作者曾对几类特殊重特征算子证明了局部存在弱解的充分条件,本文将进一步证明对一般定重特征算子局部可解的充分条件。     

带变号势函数的分数阶p-Laplacian方程弱解的存在性

研究了一类分数阶p-Laplacian方程(-Δ)_p~su+V(x)|u|~(p-2)u=f(x,u),x∈R~N弱解的存在性问题.其中:p≥2;N≥2;s∈(0,1);V(x)∈C(RN)是变号的势函数;(-Δ)sp是分数阶p-Laplacian算子;非线性项f:RN×R→R是Carathéodory泛函.运用山路引理,建立了该方程非平凡弱解的存在性定理.     

一类椭圆方程弱解的存在性问题

研究一类椭圆方程弱解的存在性,获得了一个弱解的无界序列的存在性定理,其中ΩСR是具有光滑边界的有界开区域,主要结果改进和发展了前人的一些相应结果.     

含p-Laplace算子的非线性方程的多解的存在性

利用变分方法证明了Neumann边值问题-△粯pu+α(x)up-2u=μf(x,u),x∈Ω5u5γ=0,x∈5在一定条件下一列弱解的存在性,其中△粯pu=div(1+èup2-2èu),p≥2,μ>0为实参数,α(x)∈L∞(Ω)且α(x)>0,f:Ω×R→R为满足一定条件的Carathoédory函数。     

具有L1初值的非牛顿多方渗流方程解的正性和熄灭性

利用比较原理和基本解证明了非牛顿多方渗流方程的解在初值u₀(x)∈L¹Ω)及零边值条件下具有正性和熄灭性, 其中m>0, p>1.     

Weak solutions of the isothermal bipolar hydrodynamic model for semiconductors with large data

This paper is devoted to weak solutions of Cauchy problem to the isothermal bipolar hydrodynamic model with large data. The model takes the bipolar Euler-Poisson form, with electric field and relaxation terms added to the momentum equations. Using Glimm scheme to the hyperbolic part and the standard theory to the ordinary differential equations, we first construct the approximation solutions, then from the facts that the total charge is quasi-conservation, we can obtain a uniform estimate of the total variation of the electric field, which allows to prove the L∞ estimate of densities and velocities, and the convergence of the scheme. Then we can prove the global existence of weal solution to Cauchy problem with large data.     

Synthesis,characterization and photoluminescence of aluminum <Emphasis Type="Italic">N</Emphasis>-aryloxo functionalized <Emphasis Type="Italic">β</Emphasis>-ketoiminate complexes

The synthesis, characterization and luminescent properties of aluminum complexes containing a dianionic N-aryloxo functionalized β-ketoiminate ligand are presented. 4-(2-Hydroxy-5-R-phenyl)imino-2-pentanone (R = Me, L¹H₂; R = tert-butyl, L²H₂) ligands reacted with AlEt₃ in tetrahydrofuran to give the aluminum complexes (L¹AlEt)₂ (1) and (L²AlEt)₂ (2) in reasonable isolated yields. X-ray diffraction revealed that complexes 1 and 2 have solvent-free centrosymmetric dimeric structures, and each aluminum center has distorted trigonal bipyramidal geometry. At room temperature, complexes 1 and 2 exhibit blue photoluminescence in acetonitrile with maximum emission wavelengths of 419 and 413 nm, respectively.     

Enolate chelating N-heterocyclic carbene complexes of Fe(II): Synthesis, structure and their catalytic activity for ring-opening polymerization of ε-caprolactone

The reaction of anhydrous FeBr2 with two equivalents of anionic N-heterocyclic carbene (NaL1 and NaL2), which are generated in situ by the reaction of the corresponding salt [4-R-C6H4COCH2{CH- (NCHCHNiPr)}Br] (R = OCH3, H2L1Br, 1; R = F, H2L2Br, 2) with two equivalents of NaN(SiMe3)2, affords bis-ligand Fe(II) complexes of L12Fe (3) and L22Fe (4) in high yield, respectively. Attempt to synthesize mono-ligand Fe(II) bromide by the 1:1 molar ratio of NaL to FeBr2 is unsuccessful, and the same com- plexes of 3 and 4 were obtained. Both 3 and 4 have been depicted by elemental analysis and X-ray structure determination. Preliminary studies show that both 3 and 4 can be used as single-component catalyst for the ring-opening polymerization of ε-caprolactone, and the catalytic activity of 3 is higher than that of 4.     

扩散占优的2×2双曲平衡律奇异松弛极限及其应用

研究一般扩散占优的2×2双曲平衡律系统奇异松弛极限, 用补偿紧性方法, 在松弛时间τ比扩散系数ε趋于零快时, 即τ=o(ε), ε→ 0时, 得到其解的整体存在性一般框架： 如果上述系统的解存在对ε一致的先验L^∞估计, 则其解序列收敛于上述系统的对应平衡状态解. 并将这一框架应用于一些具有非齐次项和松弛项的重要非线性系统, 如有非齐次项和松弛项的二次流、 LeRoux系统、 非线性弹性系统和交 通扩展流等.     

The boundedness of singular integral operator along an open curve

It is well known that, the singular integral operatorS defined as: ifL is a closed smooth contour in the complex plane C, thenS is a bounded linear operator fromH ^μ(L) intoH ^μ(L): ifL is an open smooth curve, thenS is just a linear operator fromH ^* intoH ^*. In this paper, we define a Banach space , and prove that is a bounded linear operator, then verify the boundedness of other kinds of singular integral operators. Supported by the National Science Foundation of China Wang Xiaolin: born in Aug. 1950, Professor     

Prescribing symmetric scalar curvature onS 2

The problem of prescribing scalar curvature in S2 is discussed, and the solvability of the e-quation - Δu + 2-Reu = 0 on S2, is given, where R∈C0(S2). It is known that there are some obstructions . Some new results are given by seeking a solution of the minimax type. For example, supposing that R is G symmetric and is constant on the set of fixed points on S2 under G (where G is a subgroup of O(3)), It is proved that the equation is solvable if and only if R is positive somewhere.     

线性交换子的加权估计

 多线性交换子T_b(f)(x)=∫_Rⁿ∏_i=1^m(b_i(x)-b_i(y))k(x,y)f(y)dy在L^p(Rⁿ)(1K是一个标准的Calderón-Zygmund核.主要研究交换子Mf(x)=sup_x∈Q∫_Q|f(y)|dy,其中f∈L_loc(Rⁿ),x∈Rⁿ,Q是任何包含x的方体,并用Sharp极大估计得到了该多线性交换子在Herz空间的一个加权有界性.     

Thermodynamic characterization of two novel spin-crossover complexes

Spin-crossover complexes are of great interest to the scientists because of their potential application in molecular-based electronic devices. Some octahedral metal compounds with 3dn (4 ≤ n ≤ 7) configuration can induce a spin state conversion through a fine tuning condition (temperature, pressure, light irradiation, etc.). If the conversion occurs reversibly with a hystersis loop and color change, it will make the system possessing memory effect. The memory effect can be magnified and the …