CONVERGENCE OF THE SCHRÖDINGER–POISSON SYSTEM TO THE INCOMPRESSIBLE EULER EQUATIONS

ABSTRACT

We study here an asymptotic limit of the Schrödinger–Poisson system. We prove that the current converges toward a dissipative solution of the Euler equations when we consider a semi-classical quasi-neutral limit. The proof involves the modulated energy introduced by Brenier in Ref. [2] Brenier, Y. 2000. Convergence of the Vlasov-Poisson System to the Incompressible Euler Equations. Comm. Partial Differential Equations, 25(3–4): 737–754. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar].     

ON THE FEFFERMAN–PHONG INEQUALITY AND RELATED PROBLEMS

ABSTRACT

The aim of this article is to provide a new approach for the classical Fefferman–Phong inequality and some other related inequalities concerning pseudodifferential operators. The idea is to conjugate these estimates with respect to the FBI transform and obtain equivalent formulations which require only a few derivatives of the symbol. Modulo some integration by parts, these are reduced to certain decomposition results for C ^{1, 1}, respectively C ^{3, 1} functions. As a byproduct of this method, we get to extend the inequalities to (possibly sharp) classes of symbols with limited smoothness.     

HOMOGENEOUS HYPERCOMPLEX STRUCTURES I–THE COMPACT LIE GROUPS

We obtain a complete list of homogeneous hypercomplex structures on the compact Lie groups. The substantial results are formulated and proved entirely in terms of the structure theory of Lie groups and algebras.     

PENALTY APPROXIMATIONS TO THE STATIONARY POWER-LAW NAVIER–STOKES PROBLEM

In this work, penalty approximations to the steady state Navier-Stokes problem governed by the the power-law model for viscous incompressible non-Newtonian flows in bounded convex domains in R^d (2 ≤ d) are studied. Existence and uniqueness of solutions to the penalty approximations are proved, convergence is shown, and rates of convergence are derived.     

THE GAUSS–GREEN THEOREM IN CLIFFORD ANALYSIS AND ITS APPLICATIONS

In this article, we establish the Gauss–Green type theorems for Clifford-valued functions in Clifford analysis. The boundary conditions in theorems obtained are very general by using the geometric measure theoretic method. The Cauchy–Pompeiu formula for Clifford-valued functions under the weak condition will be derived as their simple application. Furthermore, Cauchy formula for monogenic functions under the weak condition is derived directly from the Cauchy–Pompeiu formula.     

THE SOLUTION TO THE SK-MODEL

IIntroductlonAs one ofwell－kn。mean ield models for spin glasses,the SK(Sherrin红on－Kirkpatri山)model has been studied by many authors恤叫2]nd[81,andthe references therein)．Particu－larl儿丁劝a以andls]repm眈* some quite lmerestingresults on It in his one－hour Invited talk tthe International Congress ofMathem航icians held t Berlin in August,ig98．In mathematical terms;the SK－Model Is the study of a cert。n random measure on Z。:＝{一1;1}”for a natural。mber N．Z。Is called configu…     

NILPOTENT ELEMENTS IN THE JACOBSON–WITT ALGEBRA OVER A FINITE FIELD

It is shown in this paper that the number of nilpotent elements in the Jacobson–Witt algebra W _n over a finite field \( {\mathbb F} \) _q is equal to the expected power of q.     

THE FINITE INVARIANT MEASURES AND THE REVERSIBLE MEASURES OF THE DIFFUSIONS WITH THE VENTZEL''''S BOUNDARY CONDITIONS IN THE CIRCULAR DISC

For a given rotation-invariant operator Ω in the unit disc, the necessary condition for thef xistence of finite invariant measures of the strong Markov transition functions determined by Ω with the Ventzel's boundary conditions of finite rank is established If only rotation-invariant transition functions are considered, then the necessary and sufficient conditions for a given measure to be invariant and to be reversible, and all the cor6esponding boundary conditions for posseusiug these properties have been found explicitly in this paper.     

THE WEAK CONCENTRATION OF THE SK-MODEL

1. Main ResultThe SK-model is one of the welLknown mean field models for spin glasses and Talagrandlllreported some advances of this model. Concretely, the SK-model can be described as follows.SK-model (without external field). For a natural nUInber N, letWhere (gij)1相似文献   

THE HAUSDORFF MEASURE FOR THE SAMPLE PATH OF THE WESTWATER PROCESS

91.IntroductionTheso-calledWestwaterprocessisthecoordinateprocessunderthepolymermeasureu(g)in3-dimensionsconstructedbyWestwater(see[7,8]),andthepolymermeasurev(g)onCo([O,1]-R')isformallydefinedbywhereC,isthenormalization,gE[o,oo)isacouplingconstant,pistheWienermeasureonCo([o,11-R').Inarecentpaper(see[9]),weprovedthattheHausdorffdimensionofthesamplepathoftheWestwaterprocess{X,,t6[O,1]}isalsotwowithprobability1tou(g).Actually,weprovedin[9]thatgh(ImX)5C,y(g)-a.e.(1.1)m(ImX)5C,y(g)-a.e.(1.…     

ON THE STABILITY OF THE RESIDUAL-FREE BUBBLES FOR THE NAVIER-STOKES EQUATIONS

This paper considers the Calerkin finite element method for the incompressible Navier-Stokes equations in two dimensions, where the finite-dimensional spaces employed consist of piecewise polynomials enriched with residual-free bubble （RFB） functions. The stability features of the residual-free bubble functions for the linearized Navier-Stokes equations are analyzed in this work. It is shown that the enrichment of the velocity space by bubble functions stabilizes the numerical method for any value of the viscosity parameter for triangular elements and for values of the viscosity parameter in the vanishing limit case for quadrilateral elements.     

THE ASYMPTOTIC FORMULA OF THE ORTHOGONAL RATIONAL FUNCTION ON THE UNIT CIRCLE

In this paper we obtained the asymptotic formula of the orthogonal rational function on the unit circlewith respect to the weight function μ(z) with preasigned poles, which are in the exterior of the unit disk.     

THE ENERGY CONSERVATION OF THE LANDAU-LIFSHITZ-BLOCH EQUATION

In this paper,we consider the three-dimensional Landau-Lifshitz-Bloch equation in the whole space,which can describe the micromagnetic dynamic behavior of material at all temperatures,especially near the Curie temperature.We establish a sufficient condition of energy conservation for when weak solutions of the Landau-Lifshitz-Bloch equation with the temperature higher than the Curie temperature and its gradient belong to the Besov space■ for some α∈(1/2,1) and p=9/3α+1.Moreover,we also use the d...     

ON THE SENSITIVITY OF THE LDU FACTORIZATION

1　IntroductionG.W.Stewart,X.-W.Chang and A.Barralund etc.have done lot of perturbationanalyses on LU,QR and Cholesky factorizations( see[5] ,[6] ,[1 ] ,[2 ] ,[4 ] ,[3 ] ) .We givesensitivity analysisfor LDU factorization in this paper.The LDU factorization ( or LDMT) is an important method in numerical linear algebra( see [7] ) ,and can be viewed as the general form for LDLT factorization. The differencebetween LDU and LU factorizations in upper triangular matrix U,i.e. U is uni…     

THE SERIES SOLUTION OF THE GEL'FAND-LEVITAN-MARCHENKO EQUATION

The convergence of the Neumann series solution of the Gel'fand-Levitan-Marchenko equation in L~∞[0, ∞), L~1[0, ∞) and L~2[0, ∞) is proved and the explicit expression of the series solution is given.     

ON THE REGULARITY OF THE MINIMUM SOLUTION OF THE RESTRAINED VARIATIONAL PROBLEMS

This paper is concerned with the regularity of minimum solution u of the following functional on the restraint Under appropriate conditions, the bounded minimum solution u of the above functional is proved to be nothing but Hlder continuous.     

THE TRANSFINITE BASIS OF THE BIDUAL SPACE OF THE LONG JAMES SPACE

A transfinite basis of the bidual space of the long James space is presented in this paper. Moreover, we prove that the space J(w+r) has the approximation property, where J (ω) is the James space, r is any finite integer.     

THE GRADED MODULES FOR THE POISSON ALGEBRAS

§0.ＩｎｔｒｏｄｕｃｔｉｏｎＡｓｗｅｋｎｏｗ,ｔｈｅｎｏｎｃｌａｓｓｉｃａｌ(ｇｒａｄｅｄ)ｓｉｍｐｌｅｍｏｄｕｌａｒＬｉｅａｌｇｅｂｒａｓｗｈｅｎｔｈｅｂａｃｋｇｒｏｕｎｄｆｉｅｌｄｉｓｏｆｃｈａｒａｃｔｅｒｉｓｔｉｃｐ>5ｈａｖｅｆｏｕｒｔｙｐｅｓ:Ｗ(ｎ,ｍ),Ｓ(ｎ,ｍ),Ｈ(ｎ,ｍ)ａｎｄＫ(ｎ,ｍ).Ｆｏｒｔｈｅｇｒａｄｅｄｍｏｄｕｌｅｓｏｆｔｈｅｆｉｒｓｔｔｈｒｅｅｔｙｐｅｓ,Ｓｈｅｎｇａｖｅａｃｏｍｐｌｅｔｅｄｅｓｃｒｉｐｔｉｏｎｂａｓｅｄｏｎｈｉｓｍｉｘｅｄｐｒｏｄｕｃｔｒｅａｌｉｚａｔｉｏｎｓｉｎ…     

ON THE CONTINUABILITY OF SOLUTIONS IN THE FUTURE FOR THE LIENARD SYSTEM

ＯＮＴＨＥＣＯＮＴＩＮＵＡＢＩＬＩＴＹＯＦＳＯＬＵＴＩＯＮＳＩＮＴＨＥＦＵＴＵＲＥＦＯＲＴＨＥＬＩＥＮＡＲＤＳＹＳＴＥＭＨｕａｎｇＬｉｈｏｎｇ（黄立宏）（ＨｕｎａｎＵｎｉｖｅｒｓｉｔｙ，湖南大学，邮编：４１００８２）Ａｂｓｔｒａｃｔ：Ｔｈｅｍａｉｎｐ...     

ON THE SPACES OF THE MAXIMAL POINTS

For a continuous domain D, some characterization that the convex powerdomain CD is a domain hull of Max(CD) is given in terms of compact subsets of D. And in this case, it is proved that the set of the maximal points Max(CD) of CD with the relative Scott topology is homeomorphic to the set of all Scott compact subsets of Max(.D) with the topology induced by the Hausdorff metric derived from a metric on Max(D) when Max(D) is metrizable.