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

convergence to nonlinear diffusion waves for solutions of a system of hyperbolic conservation laws with damping we consider a model of hyperbolic conservation laws with damping and show that the solutions tend to those of a nonlinear parabolic equation time asymptotically the hyperbolic model may be viewed as isentropic euler equations with friction term added to the momentum equation to model gas flow through a porous media in this case our result justifies darcy s law time asymptotically our model may also be viewed as an elastic model with damping

a class of parallel two level nonlinear schwarz preconditioned inexact newton algorithms we propose and test a new class of two level nonlinear additive schwarz preconditioned inexact newton algorithms aspin the two level aspin combines a local nonlinear additive schwarz preconditioner and a global linear coarse preconditioner this approach is more attractive than the two level method introduced in cai keyes and marcinkowski nonlinear additive schwarz preconditioners and applications in computational fluid dynamics international journal numerical methods in fluids 40 2002 1463 1470 which is nonlinear on both levels since the coarse part of the global function evaluation requires only the solution of a linear coarse system rather than a nonlinear coarse system derived from the discretization of original partial dierential equations the overall computational cost is reduced considerably our parallel numerical results based on an incompressible lid driven flow problem show that the new two level aspin is quite scalable with respect to the number of processors and the fine mesh size when the coarse mesh size is fine enough and in addition the convergence is not sensitive to the reynolds numbers

robust feti dp methods for heterogeneous three dimensional elasticity problems iterative substructuring methods with lagrange multipliers are considered for heterogeneous linear elasticity problems with large discontinuities in the material stiffnesses in particular results for algorithms belonging to the family of dual primal feti methods are presented the core issue of these algorithms is the construction of an appropriate global problem in order to obtain a robust method which converges independently of the material discontinuities in this article several necessary and sufficient conditions arising from the theory are numerically tested and confirmed furthermore results of numerical experiments are presented for situations which are not covered by the theory such as curved edges and material discontinuities not aligned with the interface and an attempt is made to develop rules for these cases

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

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

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 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

efficient and accurate numerical methods for the klein gordon schrodinger equations in this paper we present efficient unconditionally stable and accurate numerical methods for approximations of the klein gordon schrodinger kgs equations with without damping terms the key features of our methods are based on i the application of a time splitting spectral discretization for a schrodinger type equation in kgs ii the utilization of fourier pseudospectral discretization for spatial derivatives in the klein gordon equation in kgs iii the adoption of solving the ordinary differential equations odes in phase space analytically under appropriate chosen transmission conditions between different time intervals or applying crank nicolson leap frog for linear nonlinear terms for time derivatives the numerical methods are either explicit or implicit but can be solved explicitly unconditionally stable and of spectral accuracy in space and second order accuracy in time moreover they are time reversible and time transverse invariant when there is no damping terms in kgs conserve or keep the same decay rate of the wave energy as that in kgs without or with a linear damping term keep the same dynamics of the mean value of the meson field and give exact results for the plane wave solution extensive numerical tests are presented to confirm the above properties of our numerical methods for kgs finally the methods are applied to study solitary wave collisions in one dimension 1d as well as dynamics of a 2d problem in kgs

inexact feti dp methods inexact feti dp domain decomposition methods are considered preconditioners based on formulations of feti dp as a saddle point problem are used which allow for an inexact solution of the coarse problem a positive definite reformulation of the preconditioned saddle point problem which also allows for approximate solvers is considered as well in the formulation that iterates on the original feti dp saddle point system it is also possible to solve the local neumann subdomain problems inexactly given good approximate solvers for the local and coarse problems convergence bounds of the same quality as for the standard feti dp methods are obtained numerical experiments which compare the convergence of the inexact methods with that of standard feti dp are shown for 2d and 3d elasticity using gmres and cg as krylov space methods based on parallel computations a comparison of one variant of the inexact feti dp algorithms and the standard feti dp method is carried out and similar parallel performance is achieved parallel scalability of the inexact variant is also demonstrated it is shown that for a very large number of subdomains and a very large coarse problem the inexact method can be superior copyright 2006 john wiley sons ltd

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

a preconditioner for substructuring based on constrained energy minimization a preconditioner for substructuring based on constrained energy minimization concepts is presented the preconditioner is applicable to both structured and unstructured meshes and offers a straightforward approach for the iterative solution of second and fourth order structural mechanics problems the approach involves constraints associated with disjoint sets of nodes on substructure boundaries these constraints provide the means for preconditioning at both the substructure and global levels numerical examples are presented that demonstrate the good performance of the method in terms of iterations compute time and condition numbers of the preconditioned equations

dual primal feti methods for three dimensional elliptic problems with heterogeneous coefficients in this paper certain iterative substructuring methods with lagrange multipliers are considered for elliptic problems in three dimensions the algorithms belong to the family of dual primal finite element tearing and interconnecting feti methods which recently have been introduced and analyzed successfully for elliptic problems in the plane the family of algorithms for three dimensions is extended and a full analysis is provided for the new algorithms particular attention is paid to finding algorithms with a small primal subspace since that subspace represents the only global part of the dual primal preconditioner it is shown that the condition numbers of several of the dual primal feti methods can be bounded polylogarithmically as a function of the dimension of the individual subregion problems and that the bounds are otherwise independent of the number of subdomains the mesh size and jumps in the coefficients these results closely parallel those of other successful iterative substructuring methods of primal as well as dual type

three level bddc in three dimensions balancing domain decomposition by constraints bddc methods are nonoverlapping iterative substructuring domain decomposition methods for the solution of large sparse linear algebraic systems arising from the discretization of elliptic boundary value problems their coarse problems are given in terms of a small number of continuity constraints for each subdomain which are enforced across the interface the coarse problem matrix is generated and factored by a direct solver at the beginning of the computation and it can ultimately become a bottleneck if the number of subdomains is very large in this paper two three level bddc methods are introduced for solving the coarse problem approximately for problems in three dimensions this is an extension of previous work for the two dimensional case edge constraints are considered in this work since vertex constraints alone which work well in two dimensions result in a noncompetitive algorithm in three dimensions some new technical tools are then needed in the analysis and this makes the three dimensional case more complicated estimates of the condition numbers are provided for two three level bddc methods and numerical experiments are also discussed

nonrelativistic limit of klein gordon maxwell to schrodinger poisson we prove that in the nonrelativistic limit c where c is the speed of light solutions of the klein gordon maxwell system on inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i converge in the energy space c 0 t h 1 to solutions of a schrodinger poisson system under appropriate conditions on the initial data this requires the splitting of the scalar klein gordon field into a sum of two fields corresponding in the physical interpretation to electrons and positrons the proof relies on bilinear spacetime estimates related to the klainerman machedon estimates but taking into account the variation of the parameter c a crucial fact is that the system has a null form structure in coulomb gauge as proved by klainerman machedon

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

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

a parallel implementation of dual primal feti methods for three dimensional linear elasticity using a transformation of basis dual primal feti methods for linear elasticity problems in three dimensions are considered these are nonoverlapping domain decomposition methods where some primal continuity constraints across subdomain boundaries are required to hold throughout the iterations whereas most of the constraints are enforced by lagrange multipliers an algorithmic framework for dual primal feti methods is described together with a transformation of basis to implement the primal constraints numerical results obtained from a parallel implementation of these algorithms applied to a model benchmark problem with structured meshes and to problems with more complicated geometries from industrial and biological applications using unstructured meshes are provided these results show that the presented dual primal feti algorithms are numerical and parallel scalable

decay property of regularity loss type for nonlinear hyperbolic elliptic system in multi dimensions abstract in this paper we study the asymptotic behavior of solutions for a hyperbolic elliptic system with a 2m order elliptic part in multi dimensional space this system is a modified version of the simplest radiating gas model and it verifies l p decay property of regularity loss type in r n the global existence and l p estimates of the solution to the cauchy problem for the hyperbolic elliptic system are obtained since the dissipative property of this system is so weak in high frequency region the usual energy method does not work well in deriving the a priori estimates for global solutions to the nonlinear problem our analysis is based on a frequency decomposition and the method of combining the green function with some time weight energy estimates

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

nonlinear localization strategies for domain decomposition methods application to post buckling analyses abstract in this paper we explore the capabilities of some nonlinear strategies based on domain decomposition for nonlinear analyses and more particularly for post buckling analyses of large slender structures after having recalled the classical newton krylov schur methods chosen here to serve as a reference we propose two versions specifically developed to treat nonlinear phenomena at the most relevant scale through nonlinear localizations per substructure all these different strategies lead to solving similar condensed problems on which we apply classical domain decomposition methods performances are discussed and comparative results in terms of convergence are presented in the case of beam frames with large rotations and local buckling

spectral theory of the klein gordon equation in pontryagin spaces in this paper we investigate an abstract klein gordon equation by means of indefinite inner product methods we show that under certain assumptions on the potential which are more general than in previous works the corresponding linear operator a is self adjoint in the pontryagin space mathcal k induced by the so called energy inner product the operator a possesses a spectral function with critical points the essential spectrum of a is real with a gap around 0 and the non real spectrum consists of at most finitely many pairs of complex conjugate eigenvalues of finite algebraic multiplicity the number of these pairs is related to the size of the potential moreover a generates a group of bounded unitary operators in the pontryagin space mathcal k finally the conditions on the potential required in the paper are illustrated for the klein gordon equation in mathbb r n they include potentials consisting of a coulomb part and an lp part with n p

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

parallelization of continuous and discontinuous galerkin dual primal isogeometric tearing and interconnecting methods abstract in this paper we investigate the parallelization of dual primal isogeometric tearing and interconnecting ieti dp type methods for solving large scale continuous and discontinuous galerkin systems of equations arising from isogeometric analysis of elliptic boundary value problems these methods are extensions of the finite element tearing and interconnecting methods to isogeometric analysis the algorithms are implemented by means of energy minimizing primal subspaces we discuss how these methods can efficiently be parallelized in a distributed memory setting weak and strong scaling studies presented for two and three dimensional problems show an excellent parallel efficiency

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

global solution and large time behavior of the 3d compressible euler equations with damping national natural science foundation of china nsaf 10976026 national natural science foundation of china 11271305

l p convergence rates of planar waves for multi dimensional euler equations with damping abstract in this paper the l p convergence rates of planar diffusion waves for multi dimensional euler equations with damping are considered the analysis relies on a newly introduced frequency decomposition and green function based energy method it is a combination of the l p estimate on the low frequency component by using an approximate green function and l 2 estimate on the high frequency component through the energy method by noticing that the low frequency component in the approximate green function has the algebraic decay which governs the large time behavior while the high frequency component has the exponential decay but with singularity their combination leads to a global algebraic decay estimate to use the decay property only of the low frequency component in the approximate green function avoids the singularity in the high frequency component so that it simplifies and improves the previous works on this system this new approach of the combination of the green function and energy method through the frequency decomposition can also be applied to the hyperbolic parabolic systems satisfying the kawashima condition and also the systems whose derivatives of the coefficients have suitable time decay properties

variational principles for eigenvalues of the klein gordon equation in this paper variational principles for eigenvalues of an abstract model of the klein gordon equation with electromagnetic potential are established they are used to characterize and estimate eigenvalues in cases where the essential spectrum has a gap around 0 even in the presence of complex eigenvalues as a consequence a comparison between eigenvalues of the klein gordon equation in rd and eigenvalues of certain schrodinger operators is obtained the results are illustrated on examples including the klein gordon equation with coulomb and square well potential

nonlinear feti dp and bddc methods new nonlinear feti dp dual primal finite element tearing and interconnecting and bddc balancing domain decomposition by constraints domain decomposition methods are introduced in all these methods in each iteration local nonlinear problems are solved on the subdomains the new approaches can significantly reduce communication and show a significantly improved performance especially for problems with localized nonlinearities compared to a standard newton krylov feti dp or bddc approach moreover the coarse space of the nonlinear feti dp methods can be used to accelerate the newton convergence it is also found that the new nonlinear feti dp and nonlinear bddc methods are not as closely related as in the linear context numerical results for the p laplace operator are presented

the lp decay estimates for the chemotaxis shallow water system abstract in this paper we consider the large time behavior of solution for the chemotaxis shallow water system in two dimension by the method of frequency decomposition first we construct the green s function of the linearized system and get the corresponding estimates for low frequency part then we introduce an energy method we named double cycle method to get the decay rate for high frequency part due to the dissipative mechanism of this system the high frequency part decays faster than the low frequency part

toward extremely scalable nonlinear domain decomposition methods for elliptic partial differential equations the solution of nonlinear problems e g in material science requires fast and highly scalable parallel solvers finite element tearing and interconnecting dual primal feti dp domain decomposition methods are parallel solution methods for implicit problems discretized by finite elements recently nonlinear versions of the well known feti dp methods for linear problems have been introduced in these methods the nonlinear problem is decomposed before linearization this approach can be viewed as a strategy to further localize computational work and to extend the parallel scalability of feti dp methods toward extreme scale supercomputers here a recent nonlinear feti dp method is combined with an approach that allows an inexact solution of the feti dp coarse problem we combine the nonlinear feti dp domain decomposition method with an algebraic multigrid amg method and thus obtain a hybrid nonlinear domain decomposition multigrid method we consider scalar nonlinear problems as well as nonlinear hyp

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

the decay rate of solution for the bipolar navier stokes poisson system in this paper the cauchy problem for the bipolar navier stokes poisson system is studied we obtain the global existence and the hs decay rate of classical solutions for this problem our approach is mainly based on the analysis of the green s function of the linearized system and some elaborate energy estimates it should be mentioned that with the help of long wave short wave decomposition the decay rate of the higher order derivatives of the solutions is obtained furthermore based on the hs decay rate of the solutions we also give the lp estimate of the solution

dual primal feti methods for linear elasticity dual primal feti methods are nonoverlapping domain decomposition methods where some of the continuity constraints across subdomain boundaries are required to hold throughout the iterations as in primal iterative substructuring methods while most of the constraints are enforced by lagrange multipliers as in one level feti methods these methods are used to solve the large algebraic systems of equations that arise in elliptic finite element problems the purpose of this article is to develop strategies for selecting these constraints which are enforced throughout the iterations such that good convergence bounds are obtained that are independent of even large changes in the stiffness of the subdomains across the interface between them the algorithms are described in terms of a change of basis that has proven to be quite robust in practice a theoretical analysis is provided for the case of linear elasticity and condition number bounds are established that are uniform with respect to arbitrarily large jumps in the young s modulus of the material and otherwise depend only polylogarithmically on the number of unknowns of a single subdomain the strategies have already proven quite successful in large scale implementations of these iterative methods 2006 wiley periodicals inc

three level bddc in two dimensions balancing domain decomposition by constraints bddc methods are non overlapping iterative substructuring domain decomposition methods for the solution of large sparse linear algebraic systems arising from discretization of elliptic boundary value problems they are similar to the balancing neumann neumann algorithm however in bddc methods a small number of continuity constraints are enforced across the interface and these constraints form a new coarse global component an important advantage of using such constraints is that the schur complements that arise in the computation will all be strictly positive definite the matrix of the coarse problem is generated and factored by direct solvers at the beginning of the computation however this problem can ultimately become a bottleneck if the number of subdomains is very large in this paper two three level bddc methods are introduced for solving the coarse problem approximately in two dimensional space while still maintaining a good convergence rate estimates of the condition numbers are provided for the two three level bddc methods and numerical experiments are also discussed copyright 2006 john wiley sons ltd

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

lp convergence rate to nonlinear diffusion waves for p system with damping abstract in this paper we study the p system with frictional damping and show that the solutions time asymptotically tend to the nonlinear diffusion waves governed by the classical darcy s law by introducing an approximate green function we obtain the optimal l p 2 p convergence rate of the solution which is a perturbation of the nonlinear diffusion wave to the hyperbolic system

global existence and large time behavior for the system of compressible adiabatic flow through porous media in r 3 abstract the system of compressible adiabatic flow through porous media is considered in r 3 in the present paper the global existence and uniqueness of classical solutions are obtained when the initial data is near its equilibrium we also show that the pressure of the system converges to its equilibrium state at the same l 2 rate 1 t 3 4 as the navier stokes equations without heat conductivity but the velocity of the system decays at the l 2 rate 1 t 5 4 which is faster than the l 2 rate 1 t 3 4 for the navier stokes equations without heat conductivity duan and ma 2008 3

the pointwise estimates of solutions for euler equations with damping in multi dimensions we study the time asymptotic behavior of solutions for the isentropic euler equations with damping in multi dimensions the global existence and pointwise estimates of the solutions are obtained furthermore we obtain the optimal lp 1 p convergence rate of the solution when it is a perturbation of a constant state our approach is based on a detailed analysis of the green function of the linearized system and some energy estimates

fluid structure algorithms based on steklov poincare operators in this paper we review some classical algorithms for fluid structure interaction problems and we propose an alternative viewpoint mutuated from the domain decomposition theory this approach yields preconditioned richardson iterations on the steklov poincare nonlinear equation at the fluid structure interface

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

pointwise estimates of solutions for the cahn hilliard equation with inertial term in multi dimensions abstract in this paper we study the pointwise estimates of solutions for the cahn hilliard equation with inertial term in multi dimensions by the green function method furthermore we obtain the l p convergence rate of the solution

large time behavior of solutions for the nonlinear wave equation with viscosity in odd dimensions abstract we study the dissipation of solutions of the cauchy problem for the nonlinear dissipative wave equation in odd multi spatial dimensions pointwise estimates of the time asymptotic shape of the solutions are obtained and shown to exhibit the generalized huygens 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

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

feti dp a dual primal unified feti method part i a faster alternative to the two level feti method the feti method and its two level extension feti 2 are two numerically scalable domain decomposition methods with lagrange multipliers for the iterative solution of second order solid mechanics and fourth order beam plate and shell structural problems respectively the feti 2 method distinguishes itself from the basic or one level feti method by a second set of lagrange multipliers that are introduced at the subdomain cross points to enforce at each iteration the exact continuity of a subset of the displacement field at these specific locations in this paper we present a dual primal formulation of the feti 2 concept that eliminates the need for that second set of lagrange multipliers and unifies all previously developed one level and two level feti algorithms into a single dual primal feti dp method we show that this new feti dp method is numerically scalable for both second order and fourth order problems we also show that it is more robust and more computationally efficient than existing feti solvers particularly when the number of subdomains and or processors is very large copyright 2001 john wiley sons ltd

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

robust and scalable domain decomposition solvers for unfitted finite element methods abstract unfitted finite element methods e g extended finite element techniques or the so called finite cell method have a great potential for large scale simulations since they avoid the generation of body fitted meshes and the use of graph partitioning techniques two main bottlenecks for problems with non trivial geometries however the linear systems that arise from these discretizations can be much more ill conditioned due to the so called small cut cell problem the state of the art approach is to rely on sparse direct methods which have quadratic complexity and are thus not well suited for large scale simulations in order to solve this situation in this work we investigate the use of domain decomposition preconditioners balancing domain decomposition by constraints for unfitted methods we observe that a straightforward application of these preconditioners to the unfitted case has a very poor behavior as a result we propose a customization of the classical bddc methods based on the stiffness weighting operator and an improved definition of the coarse degrees of freedom in the definition of the preconditioner these changes lead to a robust and algorithmically scalable solver able to deal with unfitted grids a complete set of complex 3d numerical experiments shows the good performance of the proposed preconditioners

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

asymptotic behavior of solutions to conservation laws with diffusion type terms of regularity gain and regularity loss abstract in this paper we study asymptotic behaviors of solutions to the cauchy problem of nonlinear conservation laws with a diffusion type source term related to an index s r for s 1 and s 1 the diffusion type term takes on a characteristic of regularity gain and regularity loss on the high frequency domain respectively by combining the green function method with the energy method we overcome the weakly dissipative structure of the equation for the case of s 1 and obtain the global existence and optimal l p norm time decay rates of solutions in the case of regularity gain pointwise estimates of solutions are shown by using the refined analysis on the green function

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

pointwise convergence to shock waves for viscous conservation laws we are interested in the pointwise behavior of the perturbations of shock waves for viscous conservation laws it is shown that besides a translation of the shock waves and of linear and nonlinear diffusion waves of heat and burgers equations a perturbation also gives rise to algebraically decaying terms which measure the coupling of waves of different characteristic families our technique is a combination of time asymptotic expansion construction of approximate green functions and analysis of nonlinear wave interactions the pointwise estimates yield optimal lp convergence of the perturbation to the shock and diffusion waves 1 p the new approach of obtaining pointwise estimates based on the green functions for the linearized system and the analysis of nonlinear wave interactions is also useful for studying the stability of waves of distinct types and nonclassical shocks these are being explored elsewhere 1997 john wiley sons inc

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

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

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

feti dp bddc and block cholesky methods the feti dp and bddc algorithms are reformulated using block cholesky factorizations an approach which can provide a useful framework for the design of domain decomposition algorithms for solving symmetric positive definite linear system of equations instead of introducing lagrange multipliers to enforce the coarse level primal continuity constraints in these algorithms a change of variables is used such that each primal constraint corresponds to an explicit degree of freedom with the new formulation of these algorithms a simplified proof is provided that the spectra of a pair of feti dp and bddc algorithms with the same set of primal constraints are essentially the same numerical experiments for a two dimensional laplace s equation also confirm this result copyright 2005 john wiley sons ltd