global existence and optimal convergence rates for the strong solutions in h 2 to the 3d viscous liquid gas two phase flow model abstract this paper is concerned with the cauchy problem of the three dimensional viscous liquid gas two phase flow model we prove the global existence of a strong solution when h 2 norm of the initial perturbation around a constant state is sufficiently small and its l 1 norm is bounded moreover the optimal convergence rates are also obtained for such a solution

weak solutions for an inviscid two phase flow model in physical vacuum abstract we investigate a free boundary problem for the inviscid two phase flow model with moving physical vacuum boundary which is a degenerate and characteristic hyperbolic system of conservation laws based on a suitable transformation a special degenerate parabolic approximation and delicate uniform energy estimates we prove the existence and uniqueness of the local weak solutions this can be regarded as a generalization of the results in coutand and shkoller 2011 5 from single phase gas model to two phase gas liquid model

on a class of functionals invariant under a zn action abstract this document considers a system of ordinary differential equations of the form q v sub q t q f t where f and v are periodic in t v is periodic in the components of q q sub 1 q sub m and the mean value of f vanishes by showing that a corresponding functional is invariant under a natural z sub n action a simple variational argument yields at least n 1 distinct periodic solutions of more general versions of are also treated as is a class of neumann problems for semilinear elliptic partial differential equations

a blow up criterion for a 2d viscous liquid gas two phase flow model abstract in this paper we prove a blow up criterion in terms of the upper bound of the liquid mass for the strong solution to the two dimensional 2d viscous liquid gas two phase flow model in a smooth bounded domain the result also applies to three dimensional 3d case

existence and uniqueness of global weak solution to a two phase flow model with vacuum in this paper we study a two phase liquid gas model with constant viscosity coefficient when both the initial liquid and gas masses connect to vacuum continuously just as in evje and karlsen commun pure appl anal 8 1867 1894 2009 and evje et al nonlinear anal 70 3864 3886 2009 the gas is assumed to be polytropic whereas the liquid is treated as an incompressible fluid we use a new technique to get the upper and lower bounds of gas and liquid masses n and m then we get the global existence of weak solution by the line method also we obtain the uniqueness of the weak solution

decay of the navier stokes poisson equations we establish the time decay rates of the solution to the cauchy problem for the compressible navier stokes poisson system via a refined pure energy method in particular the optimal decay rates of the higher order spatial derivatives of the solution are obtained the h s 0 s 3 2 negative sobolev norms are shown to be preserved along time evolution and enhance the decay rates as a corollary we also obtain the usual lp l2 1 p 2 type of the optimal decay rates compared to the compressible navier stokes system and the compressible irrotational euler poisson system our results imply that both the dispersion effect of the electric field and the viscous dissipation contribute to enhance the decay rate of the density our proof is based on a family of scaled energy estimates with minimum derivative counts and interpolations among them without linear decay analysis

decay estimates of solutions for the equations of motion of compressible viscous and heat conductive gases in an exterior domain in ℝ3 we consider the equations of motion of compressible viscous and heat conductive gases in an exterior domain in 3 we give the l q l p estimates for solutions to the linearized equations and show an optimal decay estimate for solutions to the nonlinear problem

a blow up criterion of strong solutions to a viscous liquid gas two phase flow model with vacuum in 3d abstract in this paper we get a blow up criterion for the strong solutions to the 3d viscous liquid gas two phase flow model with vacuum more precisely we prove that the bound of l t 1 l x norm of the deformation tensor of velocity gradient controls the possible breakdown of the strong solutions

existence and multiplicity for solutions of neumann problem for semilinear elliptic equations the existence and multiplicity results are obtained for solutions of neumann problem for semilinear elliptic equations by the least action principle and the minimax methods respectively

global existence of weak solutions for a viscous two phase model abstract the purpose of this paper is to explore a viscous two phase liquid gas model relevant for well and pipe flow our approach relies on applying suitable modifications of techniques previously used for studying the single phase isothermal navier stokes equations a main issue is the introduction of a novel two phase variant of the potential energy function needed for obtaining fundamental a priori estimates we derive an existence result for weak solutions in a setting where transition to single phase flow is guaranteed not to occur when the initial state is a true mixture of both phases some numerical examples are also included in order to demonstrate characteristic behavior of solutions in particular we illustrate how two phase flow is genuinely different compared to single phase flow concerning the behavior of an initial mass discontinuity

pairs of nontrivial solutions for resonant neumann problems abstract we study a semilinear neumann problem which is resonant at with respect to any eigenvalue different from the first and the second eigenvalue of n the negative neumann laplacian using a combination of variational methods with morse theoretic techniques we show that the problem has at least two nontrivial smooth solutions

the pointwise estimates of diffusion wave for the navier stokes systems in odd multi dimensions we study the dissipation of solutions of the isentropic navier stokes equations in odd multi dimensions pointwise estimates of the time asymptotic shape of the solutions are obtained and shown to exhibit the generalized huygen s principle our approach is based on the detailed analysis of the green function of the linearized system this is used to study the coupling of nonlinear diffusion waves

optimal lp lq convergence rates for the compressible navier stokes equations with potential force in this paper we are concerned with the optimal lp lq convergence rates for the compressible navier stokes equations with a potential external force in the whole space under the smallness assumption on both the initial perturbation and the external force in some sobolev spaces the optimal convergence rates of the solution in lq norm with 2 q 6 and its first order derivative in l2 norm are obtained when the initial perturbation is bounded in lp with 1 p 6 5 the proof is based on the energy estimates on the solution to the nonlinear problem and some lp lq estimates on the semigroup generated by the corresponding linearized operator

an example of a generalized brownian motion we present an example of a generalized brownian motion it is given by creation and annihilation operators on a twisted fock space ofl2 these operators fulfill for a fixed 1 1 the relationsc f c g c g c f f g 1 f g l2 we show that the distribution of these operators with respect to the vacuum expectation is a generalized gaussian distribution in the sense that all moments can be calculated from the second moments with the help of a combinatorial formula we also indicate that our brownian motion is one component of ann dimensional brownian motion which is invariant under the quantum groups u n of woronowicz with v2

realizability of a model in infinite statistics following greenberg and others we study a space with a collection of operatorsa k satisfying the q mutator relations a l a k a l k l corresponding forq 1 to classical bose and fermi statistics we show that then n matrixa n q representing the scalar products ofn particle states is positive definite for alln ifq lies between 1 and 1 so that the commutator relations have a hilbert space representation in this case this has also been proved by fivel and by bozejko and speicher we also give an explicit factorization ofa n q as a product of matrices of the form 1 q jt 1 with 1 j n andt a permutation matrix in particular a n q is singular if and only ifq m 1 for some integerm of the formk 2 k 2 k n

stochastic integration with respect to q brownian motion we develop a stochastic integration with respect to a q brownian motion for i e a non commutative process where the operator at and its adjoint fulfill the q commutation relation under the vacuum state expectation we show that this process enjoys a predictable representation type property

a q deformed poisson distribution based on orthogonal polynomials we introduce certain q deformations of the binomial distribution and the poisson distribution by virtue of q deformed sequences of orthogonal polynomials they correspond to the case of free independence for q 0 and are reduced to the usual commutative case when q 1 furthermore we determine the probability measure for a q deformed poisson distribution by using the formulae for the al salam chihara polynomials of askey and ismail

global strong solution for a three dimensional viscous liquid gas two phase flow model with vacuum this paper is concerned with the cauchy problem of the 3d viscous liquid gas two phase flow model where the initial vacuum is allowed the existence of the global strong solution is proved when the energy of the initial data is small enough

large time behavior of solutions for compressible euler equations with damping in r 3 we consider the long time behavior and optimal decay rates of global strong solutions for the isentropic compressible euler equations with damping in r3 in the present paper when the regular initial data belong to some sobolev space hl r3 b 1 s r3 with l 4 and s 0 1 we show that the density of the system converges to its equilibrium state at the rates 1 t 34 s2 in the l2 norm or 1 t 32 s2 in the l norm respectively the momentum of the system decays at the rates 1 t 54 s2 in the l2 norm or 1 t 2 s2 in the l norm respectively which are shown to be optimal for the compressible euler equations with damping

a real space renormalization approach to the kubo greenwood formula in mirror fibonacci systems an exact real space renormalization method is developed to address the electronic transport in mirror fibonacci chains at a macroscopic scale by means of the kubo greenwood formula the results show that the mirror symmetry induces a large number of transparent states in the dc conductivity spectra contrary to the simple fibonacci case a length scaling analysis over ten orders of magnitude reveals the existence of critically localized states and their ac conduction spectra show a highly oscillating behaviour for multidimensional quasiperiodic systems a novel renormalization plus convolution method is proposed this combined renormalization convolution method has shown an extremely elevated computing efficiency being able to calculate electrical conductance of a three dimensional non crystalline solid with 10 30 atoms finally the dc and ac conductances of mirror fibonacci nanowires are also investigated where a quantized dc conductance variation with the fermi energy is found as observed in gold nanowires

q gaussian processes non commutative and classical aspects we examine for 1 q 1 q gaussian processes i e families of operators non commutative random variables where the a t fulfill the q commutation relations for some covariance function equipped with the vacuum expectation state we show that there is a q analogue of the gaussian functor of second quantization behind these processes and that this structure can be used to translate questions on q gaussian processes into corresponding and much simpler questions in the underlying hilbert space in particular we use this idea to show that a large class of q gaussian processes possesses a non commutative kind of markov property which ensures that there exist classical versions of these non commutative processes this answers an old question of frisch and bourret fb

existence and continuation of solutions for a nonlinear neumann problem abstract in this article we study the existence continuation and bifurcation from infinity of nonconstant solutions for a nonlinear neumann problem we apply the leray schauder degree and the degree for s o 2 equivariant gradient operators defined by the second author in s rybicki s o 2 degree for orthogonal maps and its applications to bifurcation theory nonlinear anal tma 23 1 1994 83 102

global existence in critical spaces for flows of compressible viscous and heat conductive gases we are concerned with global existence and uniqueness of strong solutions for a general model of viscous and heat conductive gases the initial data are supposed to be close to a stable equilibrium with constant density and temperature using uniform estimates for the linearized system with a convection term we get global well posedness in a functional setting invariant with respect to the scaling of the associated equations in space dimension n 3 we also show a smoothing effect on the velocity and the temperature and a decay on the difference between the density and the constant reference state these results extend a previous paper devoted to the barotropic case see 5

existence of a nontrivial solution for a class of hemivariational inequality problems at double resonance abstract in this paper we discuss a class of semilinear elliptic hemivariational inequality problems by using the nonsmooth minimax principle for locally lipschitz functions we establish the existence of a nontrivial solution for the semilinear elliptic hemivariational inequality problem where incomplete double resonance occurs at infinity between two distinct consecutive eigenvalues

fourth moment theorem and q brownian chaos in 2005 nualart and peccati ann probab 33 1 177 193 2005 proved the so called fourth moment theorem asserting that for a sequence of normalized multiple wiener ito integrals to converge to the standard gaussian law it is necessary and sufficient that its fourth moment tends to 3 a few years later kemp et al ann probab 40 4 1577 1635 2011 extended this theorem to a sequence of normalized multiple wigner integrals in the context of the free brownian motion the q brownian motion q in 1 1 introduced by the physicists frisch and bourret j math phys 11 364 390 1970 in 1970 and mathematically studied by bozejko and speicher commun math phys 137 519 531 1991 interpolates between the classical brownian motion q 1 and the free brownian motion q 0 and is one of the nicest examples of non commutative processes the question we shall solve in this paper is the following what does the fourth moment theorem become when dealing with a q brownian motion

nonlinear boundary value problems at resonance soit un espace de mesure fini et h l 2 l espace des fonctions a valeurs reelles de carre integrable mesurables de lebesgue sur on considere l equation lu r n u g u h ou h h l dom l h h est un operateur lineaire auto adjoint densement defini r n appartient au spectre l g r r est une fonction qui peut etre non lineaire on donne des resultats d existence generaux

free monotone transport by solving a free analog of the monge ampere equation we prove a non commutative analog of brenier s monotone transport theorem if an n tuple of self adjoint non commutative random variables z 1 z n satisfies a regularity condition its conjugate variables 1 n should be analytic in z 1 z n and j should be close to z j in a certain analytic norm then there exist invertible non commutative functions f j of an n tuple of semicircular variables s 1 s n so that z j f j s 1 s n moreover f j can be chosen to be monotone in the sense that and g is a non commutative function with a positive definite hessian in particular we can deduce that c z 1 z n c s 1 s n and w z 1 dots z n cong l mathbb f n thus our condition is a useful way to recognize when an n tuple of operators generate a free group factor we obtain as a consequence that the q deformed free group factors vargamma q mathbb r n are isomorphic for sufficiently small q with bound depending on n to free group factors we also partially prove a conjecture of voiculescu by showing that free gibbs states which are small perturbations of a semicircle law generate free group factors lastly we show that entrywise monotone transport maps for certain gibbs measure on matrices are well approximated by the matricial transport maps given by free monotone transport

hypercontractivity in non commutative holomorphic spaces we prove an analog of janson s strong hypercontractivity inequality in a class of non commutative holomorphic algebras our setting is the q gaussian algebras q associated to the q fock spaces of bozejko kummerer and speicher for q 1 1 we construct subalgebras open image in new window a q segal bargmann transform and prove janson s strong hypercontractivity open image in new window for r an even integer

global weak solutions for a viscous liquid gas model with transition to single phase gas flow and vacuum abstract this work deals with a viscous two phase liquid gas model relevant to the flow in wells and pipelines the liquid is treated as an incompressible fluid whereas the gas is assumed to be polytropic the model is rewritten in terms of lagrangian coordinates and is studied in a free boundary setting where the liquid and gas masses are of compact support initially and continuous at the boundary consequently the initial masses involve a transition to single phase gas flow and vacuum at the boundary an appropriate balance between pressure and viscous forces is identified which allows obtaining pointwise upper and lower estimates of masses these estimates rely on the assumption of a certain relation between the rate of degeneracy of the viscosity coefficient and the rate that determines how fast the initial masses are vanishing at the boundary by combining these estimates with basic energy type of estimates higher order regularity estimates are obtained the existence of global weak solutions is then proved by showing compactness for a class of semi discrete approximations

global weak solutions for a compressible gas liquid model with well formation interaction abstract the objective of this work is to explore a compressible gas liquid model designed for modeling of well flow processes we build into the model well reservoir interaction by allowing flow of gas between well and formation surrounding reservoir inflow of gas and subsequent expansion of gas as it ascends towards the top of the well a so called gas kick represents a major concern for various well operations in the context of petroleum engineering we obtain a global existence result under suitable assumptions on the regularity of initial data and the rate function that controls the flow of gas between well and formation uniqueness is also obtained by imposing more regularity on the initial data the key estimates are to obtain appropriate lower and upper bounds on the gas and liquid masses for that purpose we introduce a transformed version of the original model that is highly convenient for analysis of the original model in particular in the analysis of the transformed model additional terms representing well formation interaction can be treated by natural extensions of arguments that previously have been employed for the single phase navier stokes model the analysis ensures that transition to single phase regions do not appear when the initial state is a true gas liquid mixture

large time behavior for the system of compressible adiabatic flow through porous media in r3 abstract the cauchy problem of the system of compressible adiabatic flow through porous media in r 3 is considered we obtain the global existence and large time behavior of the solution when the initial data is close to its equilibrium in h 3 norm this is a continuing work of 31 where due to non dissipative property of the entropy s an additional assumption that the initial data is bounded in l 1 norm plays a key role in closing the a priori energy estimates and hence establishing the global existence of the solution in this paper to remove this assumption we first decompose the solution u into high frequency part u h and low frequency part u l then by constructing delicate energy functionals for u h and optimal decay rates for u l we can get the desired energy estimates to close the a priori assumption furthermore we get the optimal l 2 l 2 decay rate of the solution and show that the velocity decays faster than the density

asymptotic behavior of the solutions to the damped compressible euler equations with vacuum abstract the asymptotic behavior of solutions of the damped compressible euler equations is conjectured to obey to the famous porous media equations pmes the previous works on this topic concern the case away from vacuum where the system is strictly hyperbolic in present paper we prove that the l entropy weak solution with vacuum obtained by the compensated compactness theory converges strongly in l loc p 1 p space to the unique similarity solution of the related pme as time goes to infinity

a global existence result for the compressible navier stokes equations in the critical l p framework the present paper is dedicated to the global well posedness issue for the barotropic compressible navier stokes system in the whole space mathbb r d with d 2 we aim at extending the work by danchin inventiones mathematicae 141 3 579 614 2000 to a critical framework which is not related to the energy space for small perturbations of a stable equilibrium state in the sense of suitable lp type besov norms we establish the global existence as a consequence like for incompressible flows one may exhibit a class of large highly oscillating initial velocity fields for which global existence and uniqueness holds true in passing we obtain new estimates for the linearized and the paralinearized systems which may be of interest for future works on compressible flows

free boundary value problem for a viscous two phase model with mass dependent viscosity abstract in this paper we study a free boundary value problem for two phase liquid gas model with mass dependent viscosity coefficient when both the initial liquid and gas masses connect to vacuum with a discontinuity this is an extension of the paper s evje k h karlsen global weak solutions for a viscous liquid gas model with singular pressure law http www irisresearch no docsent emp nsf wvansatte sev just as in s evje k h karlsen global weak solutions for a viscous liquid gas model with singular pressure law http www irisresearch no docsent emp nsf wvansatte sev the gas is assumed to be polytropic whereas the liquid is treated as an incompressible fluid we give the proof of the global existence and uniqueness of weak solutions when 0 1 which have improved the previous result of evje and karlsen and get the asymptotic behavior result also we obtain the regularity of the solutions by energy method

global well posedness for systems of hyperbolic parabolic composite type with center manifold abstract concerning the global existence of classical solution to systems of hyperbolic parabolic composite type a well known general theory was established by kawashima in 4 where the dissipation condition kawashima shizuta condition to the linearized system plays a fundamental role recently systems with much weaker dissipations have attracted a lot of attentions see 1 2 10 11 among others the typical feature of this kind of system is that the corresponding linearized system has one eigenvalue with the real part equals to zero this violates the kawashima shizuta stability conditions in this paper we develop a general global well posedness theory for this kind of system moreover as the applications of the general theory several examples are given

fock space associated to coxeter groups of type b abstract in this article we construct a generalized gaussian process coming from coxeter groups of type b it is given by creation and annihilation operators on an q fock space which satisfy the commutation relation b q x b q y q b q y b q x x y i x y q 2 n where x y are elements of a complex hilbert space with a self adjoint involution x x and n is the number operator with respect to the grading on the q fock space we give an estimate of the norms of creation operators we show that the distribution of the operators b q x b q x with respect to the vacuum expectation becomes a generalized gaussian distribution in the sense that all mixed moments can be calculated from the second moments with the help of a combinatorial formula related with set partitions our generalized gaussian distribution is associated to the orthogonal polynomials called the q meixner pollaczek polynomials yielding the q hermite polynomials when 0 and free meixner polynomials when q 0

on resonant neumann problems we consider semilinear neumann problems at resonance and prove existence and multiplicity theorems the existence theorems allow resonance with respect to any eigenvalue of the negative neumann laplacian the multiplicity theorems concern problems resonant at 0 the principal eigenvalue or at the first nonzero eigenvalue our approach uses tools from critical point theory and from morse theory

blow up criterion for 3d viscous liquid gas two phase flow model abstract this work deals with the blow up criterion for the strong solution to the three dimensional viscous liquid gas two phase flow model in terms of the l 1 0 t l norm of the gradient of the velocity with two types of boundary conditions the dirichlet boundary condition and the navier slip boundary condition there is no extra restriction on viscosity coefficients the result also applies to the whole space case

large time behavior for the system of a viscous liquid gas two phase flow model in r3 abstract the cauchy problem of a three dimensional compressible viscous liquid gas two phase flow model is considered in the present paper the global existence and uniqueness of solutions are established when the initial data is close to its equilibrium in the framework of sobolev space h 3 r 3 moreover the optimal l 2 l 2 convergence rates are also obtained for the solution

some estimates of solutions for the equations of motion of compressible viscous fluid in the three dimensional exterior domain abstract we consider the equations of motion of compressible viscous fluid in an exterior domain in r 3 we give the l q l p estimates for solutions to the linearized equations and show an optimal decay estimate for solutions to the nonlinear problem in particular we shall give l 1 estimates which implies the diffusion wave of compressible navier stokes flow

type b gaussian statistics as noncommutative central limits abstract we show that the noncommutative central limit theorem of speicher can be adapted to produce the gaussian statistics associated to coxeter groups of type b in the sense of bozejko ejsmont and hasebe viewed through the lens of central limits the passage from q gaussian statistics associated with symmetric groups to the gaussian statistics associated with coxeter groups of type b is precisely the passage from a sequence of independent elements that pairwise commute or anticommute to a coupled pair of such sequences the results pave the way for the transfer of known results from the bosonic fermionic settings to such broader contexts

initial boundary value problems for the equations of motion of compressible viscous and heat conductive fluids the equations of motion of compressible viscous and heat conductive fluids are investigated for initial boundary value problems on the half space and on the exterior domain of any bounded region the global solution in time is proved to exist uniquely and approach the stationary state ast provided the prescribed initial data and the external force are sufficiently small

existence and asymptotic behavior of c1 solutions to the multi dimensional compressible euler equations with damping abstract in this paper the existence and asymptotic behavior of c 1 solutions to the multi dimensional compressible euler equations with damping on the framework of besov space are considered comparing with the well posedness results of sideris thomases wang t sideris b thomases d h wang long time behavior of solutions to the three dimensional compressible euler with damping comm partial differential equations 28 2003 953 978 we weaken the regularity assumptions on the initial data the global existence lies on a crucial a priori estimate which is obtained by the spectral localization method the main analytic tools are the littlewood paley decomposition and bony s paraproduct formula

global existence in critical spaces for compressible navier stokes equations we investigate global strong solutions for isentropic compressible fluids with initial data close to a stable equilibrium we obtain the existence and uniqueness of a solution in a functional setting invariant by the scaling of the associated equations more precisely the initial velocity has the same critical regularity index as for the incompressible homogeneous navier stokes equations and one more derivative is needed for the density we point out a smoothing effect on the velocity and a l 1 decay on the difference between the density and the constant reference state the proof lies on uniform estimates for a mixed hyperbolic parabolic linear system with a convection term

optimal hypercontractivity for fermi fields and related non commutative integration inequalities optimal hypercontractivity bounds for the fermion oscillator semigroup are obtained these are the fermion analogs of the optimal hypercontractivity bounds for the boson oscillator semigroup obtained by nelson in the process several results of independent interest in the theory of non commutative integration are established

compressible navier stokes equations with zero heat conductivity abstract we study the large time behavior of solutions of the compressible navier stokes equations without heat conductivity acoustic waves are dissipative due to the viscosity entropy waves are nondissipative due to lack of heat conductivity thus the system is of composite type the simplest prototype of this class of nonlinear partial differential equations we study the nonlinear interactions of waves using a combination of energy method weighted energy method and pointwise estimates

existence and multiplicity results to neumann problems for elliptic equations involving the p laplacian abstract in this paper existence results of positive solutions to a neumann problem involving the p laplacian are established multiplicity results are also pointed out the approach is based on variational methods

multiple solutions of a class of neumann problem for semilinear elliptic equations abstract the multiplicity results are obtained for solutions of the neumann problem for nonlinear elliptic equations with unbounded nonlinearity by the implicit function theorem and the morse theory

on the wave structure of two phase flow models we explore the relationship between two common two phase flow models usually denoted as the two fluid and drift flux models they differ in their mathematical description of momentum transfer between the phases in this paper we provide a framework in which these two model formulations are unified the drift flux model employs a mixture momentum equation and treats interphasic momentum exchange indirectly through the slip relation which gives the relative velocity between the phases as a function of the flow parameters this closure law is in general highly complex which makes it difficult to analyze the model algebraically to facilitate the analysis we express the quasi linear formulation of the drift flux model as a function of three parameters the derivatives of the slip with respect to the vector of unknown variables the wave structure of this model is investigated using a perturbation technique then we rewrite the drift flux model with a general slip relation such that it is expressed in term

multiplicity of solutions for resonant neumann problems with an indefinite and unbounded potential we examine semilinear neumann problems driven by the laplacian plus an unbounded and indefinite potential the reaction is a caratheodory function which exhibits linear growth near we allow for resonance to occur with respect to a nonprincipal nonnegative eigenvalue and we prove several multiplicity results our approach uses critical point theory morse theory and the reduction method the lyapunov schmidt method