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

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

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

configurational properties of dilute polymer solutions dimensionality and perturbation theory by using second order perturbation theory in the small parameter epsilon 4 d to 0 the author determines a specific value of the excluded volume parameter u equivalent to the fixed point value given by renormalisation group theory for this value of the excluded volume parameter each expansion series in epsilon can be summed to an exponential function the author thus studies the total number of configurations c the number of configurations returning to the origin u and the mean square end to end distance r2 of the polymer coil an interdimensional relationship developed by kosmas and freed 1978 is used to extrapolate the authors results to lower dimensions finally the author compares his results with those of previous theories and lattice enumerations discussing possible differences between the gaussian excluded volume model used by him and the self avoiding walk model close to dimensionality d 1

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

the radius of gyration of a branch of a uniform star polymer the authors use monte carlo methods and perturbation calculations to study the mean square radius of gyration of a branch of a uniform star with excluded volume as a function of the number f of branches and of the number n of monomers per branch they show that the mean square radius of gyration s n f 2 scales like a f n2v f fixed n to infinity where the exponent is independent of f they estimate the amplitude ratios a f a 1 for various values of f and show that these ratios are lattice independent the amplitude ratio increases as f increases but the effect is small the numerical agreement between the two methods is good especially for small values of f

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

lattice models of branched polymers statistics of uniform stars the authors investigate the statistical properties of uniform star polymers with f branches modelled on lattices in two and three dimensions it is shown that the growth constant exists and is equal to mu f where mu is the self avoiding walk limit the f dependence of the corresponding critical exponent gamma f is studied using exact enumeration and monte carlo techniques and the results are compared with the predictions of miyake and freed 1983 obtained using chain conformation space renormalisation group method

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

existence of sign changing solutions for an equation with a weighted p laplace operator we consider radial solutions of a general elliptic equation involving a weighted p laplace operator with a subcritical nonlinearity by a shooting method we prove the existence of solutions with any prescribed number of nodes the method is based on a change of variables in the phase plane a very general computation of an angular velocity and new estimates for the decay of an energy associated with an asymptotic hamiltonian problem estimating the rate of decay for the energy requires a sub criticality condition the method covers the case of solutions which are not compactly supported or which have compact support in the last case we show that the size of the support increases with the number of nodes

on continuity and compactness of some nonlinear operators associated with differential equations in noncompact intervals soit x t f t x t t j x s ou jcr est un intervalle donne f j r n r n est une fonction continue et s un sous ensemble de c j r n l espace des fonctions continues de j dans r n on considere l equation operateur associee x t x ou t est un operateur non lineaire discontinu dans son domaine

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

dimensions of the branches of a uniform brush polymer excluded volume effects increase the dimensions of the various branches of a uniform brush polymer to different extents the authors use monte carlo methods and perturbation calculations to study the mean square end to end branch lengths of a uniform brush with two branch points as a function of the number n of monomers in a branch and the functionalities f1 and f2 of the branch points the mean square end to end length rn2 of a branch scales like bn2v and they investigate how the amplitude b varies for the different types of branch as f1 and f2 vary the amplitude ratios are expected to be lattice independent and they find good agreement between their numerical estimates of these ratios from perturbation and monte carlo calculations they have extended the perturbation calculations to make predictions for the corresponding amplitude ratios for the mean square radii of gyration of the various branches

asymptotic stability of the compressible gas liquid model with well formation interaction and gravity abstract in this paper we are concerned with the initial boundary value problem of the compressible gas liquid model with well formation interaction and gravity the asymptotic behavior of solutions to steady states is established also the time decay rates of perturbed solutions in the sense of l norm are obtained under some suitable assumptions on the initial date if 1 associated with pressure law of gas and 0 2 0 0 3 where characterizes the viscosity coefficient and describes the mass decay rate at the boundary a main purpose of this work is to clarify the role played by the well reservoir interaction term the analysis demonstrates that it is essential to take into account information about sign as well as size of the interaction term in order to obtain time independent estimates when it operates in combination with gravity

multiple positive solutions to elliptic boundary blow up problems abstract we prove the existence of multiple positive radial solutions to the sign indefinite elliptic boundary blow up problem u a x a x g u 0 x 1 u x x 1 where g is a function superlinear at zero and at infinity a and a are the positive negative part respectively of a sign changing function a and 0 is a large parameter in particular we show how the number of solutions is affected by the nodal behavior of the weight function a the proof is based on a careful shooting type argument for the equivalent singular ode problem as a further application of this technique the existence of multiple positive radial homoclinic solutions to u a x a x g u 0 x r n is also considered

global solutions of the navier stokes equations for multidimensional compressible flow with discontinuous initial data abstract we prove the global existence of weak solutions of the navier stokes equations for compressible isothermal flow in two and three space dimensions when the initial density is close to a constant in l 2 and l and the initial velocity is small in l 2 and bounded in l 2 n in two dimensions the l 2 norms must be weighted slightly a great deal of qualitative information about the solution is obtained for example we show that the velocity and vorticity are relatively smooth in positive time as is the effective viscous flux f which is the divergence of the velocity minus a certain multiple of the pressure we find that f plays a crucial role in the entire analysis particularly in closing the required energy estimates understanding rates of regularization near the initial layer and most important obtaining time independent pointwise bounds for the density

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

weak solutions of a two phase navier stokes model with a general slip law abstract this work is devoted to a study of a gas liquid navier stokes model with a general slip law that allows the two phases to flow with unequal fluid velocity the slip law is general enough to describe counter current flow i e a situation where gas and liquid move in opposite direction motivated by applications in the context of wellbore flow systems we assume that there is a free interface which separates the gas liquid mixture region from a strongly gas dominated region which holds a specified positive pressure p the slip law is incorporated in the mass and momentum equations resulting in a model where flow is described in terms of the gas velocity however the mixture momentum equation contains a generalized pressure law composed of the standard pressure function combined with three new terms that depend on parameters characterizing the difference between gas and liquid velocity these new terms make the analysis challenging by carefully exploiting the positive external pressure p we are able to obtain uniform lower and upper bounds on a pressure related quantity this in turn allows for various higher order regularity estimates which imply that global existence and uniqueness of weak solutions can be shown

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

ground state solutions to nonlinear equations with p laplacian abstract we investigate the existence of positive radial solutions for a nonlinear elliptic equation with p laplace operator and sign changing weight both in superlinear and sublinear case we prove the existence of solutions u which are globally defined and positive outside a ball of radius r satisfy fixed initial conditions u r c 0 u r 0 and tend to zero at infinity our method is based on a fixed point result for boundary value problems on noncompact intervals and on asymptotic properties of suitable auxiliary half linear differential equations the results are new also for the classical laplace operator and may be used for proving the existence of ground state solutions and decaying solutions with exactly k zeros which are defined in the whole space some examples illustrate our results

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

existence of a ground state solution for an elliptic problem with critical growth in an exterior domain abstract in this work we prove the existence of a radially symmetric ground state solution for an elliptic equation in an exterior of a ball with neumann boundary condition

existence of global weak solution for a reduced gravity two and a half layer model we investigate the existence of global weak solution to a reduced gravity two and a half layer model in one dimensional bounded spatial domain or periodic domain also we show that any possible vacuum state has to vanish within finite time then the weak solution becomes a unique strong one

ground state solution for a problem with mean curvature operator in minkowski space abstract in this paper we prove the existence of a radial ground state solution for a quasilinear problem involving the mean curvature operator in minkowski space