a blow up criterion for two dimensional compressible viscous heat conductive flows abstract we establish a blow up criterion in terms of the upper bound of the density and temperature for the strong solution to 2d compressible viscous heat conductive flows the initial vacuum is allowed

on the existence of local strong solutions to chemotaxis shallow water system with large data and vacuum abstract in this paper motivated by the chemotaxis navier stokes system arising from mathematical biology 43 a modified shallow water type chemotactic model is derived for large initial data allowing vacuum the local existence of strong solutions together with the blow up criterion is established

strong convergence to global solutions for multidimensional flows of compressible viscous fluids with polytropic equations of state and discontinuous initial data we extend to general polytropic pressures p k 1 the existence theory of 8 for isothermal 1 flows of navier stokes fluids in two and three space dimensions with fairly general initial data specifically we require that the initial density be close to a constant in l2 and l and that the initial velocity be small in l2 and bounded in l2n in two dimensions the l2 norms must be weighted slightly solutions are obtained as limits of approximate solutions corresponding to mollified initial data the key point is that the approximate densities are shown to converge strongly so that nonlinear pressures can be accommodated even in the absence of any uniform regularity information for the approximate densities

estimating rate constants in hidden markov models by the em algorithm the em algorithm e g the baum welch 1970 re estimation is an important tool for parameter estimation in discrete time hidden markov models we present a direct re estimation of rate constants for applications in which the underlying markov process is continuous in time previous estimation of discrete time transition probabilities is not necessary

on spherically symmetric solutions of the compressible isentropic navier stokes equations we prove the global existence of weak solutions to the cauchy problem for the compressible isentropic navier stokes equations in n n 2 3 when the cauchy data are spherically symmetric the proof is based on the exploitation of the one dimensional feature of symmetric solutions and use of a new multidimensional property induced by the viscous flux the present paper extends lions existence theorem 15 to the case 1 n for spherically symmetric initial data where is the specific heat ratio in the pressure n 3 2 for n 2 and n 9 5 for n 3 dedicated to professor rolf leis on the occasion of his 70th birthday

a quantization property for static ginzburg landau vortices for any critical point of the complex ginzburg landau functional in dimension 3 we prove that for large coupling constants if the energy of this critical point on a ball of a given radius r is relatively small compared to r log then the ball of half radius contains no vortex the modulus of the solution is larger than we then show how this property can be applied to describe limiting vortices as e 0 2001 john wiley sons inc

global weak solutions to a two dimensional compressible mhd equations of viscous non resistive fluids abstract we consider a two dimensional mhd model describing the evolution of viscous compressible and electrically conducting fluids under the action of vertical magnetic field without resistivity existence of global weak solutions is established for any adiabatic exponent 1 inspired by the approximate scheme proposed in 15 we consider a two level approximate system with artificial diffusion and pressure term at the first level we prove global well posedness of the regularized system and establish uniform in e estimates to the regular solutions at the second level we show global existence of weak solutions to the system with artificial pressure by sending e to 0 and deriving uniform in estimates then global weak solution to the original system is constructed by vanishing the key issue in the limit passage is the strong convergence of approximate sequence of the density and magnetic field this is accomplished by following the technique developed in 15 26 and using the new technique of variable reduction developed by vasseur et al 33 in the context of compressible two fluid model so as to handle the cross terms

quasi neutral limit for a model of viscous plasma we perform a rigorous analysis of the quasi neutral limit for a model of viscous plasma represented by the navier stokes poisson system of equations it is shown that the limit problem is the navier stokes system describing a barotropic fluid flow with the pressure augmented by a component related to the nonlinearity in the original poisson equation

global existence of strong solutions of navier stokes equations with non newtonian potential for one dimensional isentropic compressible fluids abstract the aim of this paper is to discuss the global existence and uniqueness of strong solution for a class of the isentropic compressible navier stokes equations with non newtonian in one dimensional bounded intervals we prove two global existence results on strong solutions of the isentropic compressible navier stokes equations the first result shows only the existence and the second one shows the existence and uniqueness result based on the first result but the uniqueness requires some compatibility condition

on the strong solutions of one dimensional navier stokes poisson equations for compressible non newtonian fluids we study the strong solutions of 1d navier stokes poisson equations for compressible non newtonian fluids in bounded intervals the model is raised from the viscous isentropic gas flow under considering an external force and the non newtonian gravitational force term by using the iterative method we prove the local existence and uniqueness of strong solutions based on some compatibility condition the main condition is that the initial density vacuum is allowed

on radially symmetric solutions of the compressible isentropic self gravitating fluid abstract in this paper we mainly prove the global existence of weak solutions to the cauchy problem for the navier stokes system of compressible isentropic self gravitating fluids in r 3 when the cauchy data are radially symmetric it extends feireisl s existence theorem ducomet et al 2001 16 to the case 4 3 3 2 for radially symmetric initial data where is the specific heat ratio in the pressure if the total mass is less than a certain critical mass this conclusion also holds for 4 3 furthermore for the case of annular domain we point out the global existence radially symmetric strong solutions when the radially symmetric initial data satisfy the compatibility condition and the initial density need not be positive

fast evaluation of the likelihood of an hmm ion channel currents with filtering and colored noise hidden markov models hmms have been used in the study of single channel recordings of ion channel currents for restoration of idealized signals from noisy recordings and for estimation of kinetic parameters a key to their effectiveness from a computational point of view is that the number of operations to evaluate the likelihood posterior probabilities and the most likely state sequence is proportional to the product of the square of the dimension of the state space and the length of the series however when the state space is quite large computations can become infeasible this can happen when the record has been lowpass filtered and when the noise is colored in this paper we present an approximate method that can provide very substantial reductions in computational cost at the expense of only a very small error we describe the method and illustrate through examples the gains that can be made in evaluating the likelihood

global spherically symmetric solutions to the equations of a viscous polytropic ideal gas in an exterior domain we consider the equations of a viscous polytropic ideal gas in the domain exterior to a ball in n n 2 or 3 and prove the global existence of spherically symmetric smooth solutions for large initial data with spherical symmetry the large time behavior of the solutions is also discussed to prove the existence we first study an approximate problem in a bounded annular domain and then obtain a priori estimates independent of the boundedness of the annular domain letting the diameter of the annular domain tend to infinity we get a global spherically symmetric solution as the limit

hyperbolic compressible navier stokes equations abstract we consider the non isentropic compressible navier stokes equations with hyperbolic heat conduction and a law for the stress tensor which is modified correspondingly by maxwell s law these two relaxations turning the whole system into a hyperbolic one are not only treated simultaneously but are also considered in a version having galilean invariance for this more complicated relaxed system the global well posedness is proved for small data moreover for vanishing relaxation parameters the solutions are shown to converge to solutions of the classical system

an em algorithm for markov modulated markov processes an expectation maximization em algorithm for estimating the parameter of a markov modulated markov process in the maximum likelihood sense is developed this is a doubly stochastic random process with an underlying continuous time finite state homogeneous markov chain conditioned on that chain the observable process is a continuous time finite state nonhomogeneous markov chain the generator of the observable process at any given time is determined by the state of the underlying markov chain at that time the parameter of the process comprises the set of generators for the underlying and conditional markov chains the proposed approach generalizes an earlier approach by ryden for estimating the parameter of a markov modulated poisson process

consistent and asymptotically normal parameter estimates for hidden markov models hidden markov models are today widespread for modeling of various phenomena it has recently been shown by leroux that the maximum likelihood estimate mle of the parameters of a such a model is consistent and local asymptotic normality has been proved by bickel and ritov in this paper we propose a new clans of estimates which are consistent asymptoti cally normal and almost as good an the mle

asymptotics for the ginzburg landau equation in arbitrary dimensions let be a bounded simply connected regular domain of rn n 2 for 0 e 1 let ue c be a smooth solution of the ginzburg landau equation in with dirichlet boundary condition ge i e formula we are interested in the asymptotic behavior of ue as e goes to zero under the assumption that ee ue m0 log e and some conditions on ge which allow singularities of dimension n 3 on

on the existence of local classical solutions to the navier stokes equations with degenerate viscosities in this paper we consider the three dimensional cauchy problem of compressible navier stokes equations with degenerate viscosities depending on density with the initial data containing vacuum at far fields we prove the local existence of regular solutions with some compatibility conditions the regular solution is classical due to the smoothing effect of the velocity u in this paper we consider the three dimensional cauchy problem of compressible navier stokes equations with degenerate viscosities depending on density with the initial data containing vacuum at far fields we prove the local existence of regular solutions with some compatibility conditions the regular solution is classical due to the smoothing effect of the velocity u

asymptotic behavior of critical points for a gross pitaevskii energy abstract in this paper we study the asymptotic behavior of critical points of a gross pitaevskii energy which is proposed as a model for rotationally forced bose einstein condensate we prove that the limiting singularity set is one dimensional rectifiable we also establish the convergence result for critical points away from limiting singularities

hidden markov processes an overview of statistical and information theoretic aspects of hidden markov processes hmps is presented an hmp is a discrete time finite state homogeneous markov chain observed through a discrete time memoryless invariant channel in recent years the work of baum and petrie 1966 on finite state finite alphabet hmps was expanded to hmps with finite as well as continuous state spaces and a general alphabet in particular statistical properties and ergodic theorems for relative entropy densities of hmps were developed consistency and asymptotic normality of the maximum likelihood ml parameter estimator were proved under some mild conditions similar results were established for switching autoregressive processes these processes generalize hmps new algorithms were developed for estimating the state parameter and order of an hmp for universal coding and classification of hmps and for universal decoding of hidden markov channels these and other related topics are reviewed

global strong solutions to radial symmetric compressible navier stokes equations with free boundary in this paper we consider the two dimensional barotropic compressible navier stokes equations with stress free boundary condition imposed on the free surface as the viscosity coefficients satisfies 2 1 we establish the existence of global strong solution for arbitrarily large spherical symmetric initial data even if the density vanishes across the free boundary in particular we show that the density is strictly positive and bounded from the above and below in any finite time if the initial density is strictly positive and the free boundary propagates along the particle path and expand outwards at an algebraic rate

low mach number limit of non isentropic magnetohydrodynamic equations in a bounded domain abstract this paper verifies the low mach number limit of the non isentropic magnetohydrodynamic equations with zero thermal coefficient in a two dimensional bounded domain with navier s slip boundary condition for velocity and perfectly conducting boundary condition for magnetic field

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

helically symmetric solutions to the 3 d navier stokes equations for compressible isentropic fluids abstract we prove the existence of global weak solutions to the navier stokes equations for compressible isentropic fluids for any 1 when the cauchy data are helically symmetric where the constant is the specific heat ratio moreover a new integrability estimate of the density in any neighborhood of the symmetry axis the singularity axis is obtained

local existence of strong solution for a class of compressible non newtonian fluids with non newtonian potential the aim of this paper is to discuss the existence and uniqueness of local solutions for a class of isentropic compressible non newtonian fluids with non newtonian potential in one dimensional bounded intervals the first difficult point in this paper is that we allow the initial vacuum another one is that the viscosity term and newtonian potential term are fully nonlinear that is the viscosity term adopts the o a ladyzhenskaya model p 2 the potential term employs the q laplace form 1

maximum likelihood based measurement of interference level and noise power for memoryless gaussian channel with deterministic interference the model of memoryless gaussian channel with deterministic interference are common in various engineering applications in this letter we propose a non data aided algorithm for joint measurement of the interference level and the noise power the algorithm applies an iterative approach based on the maximum likelihood criterion the cramer rao bound crb is also derived as the performance benchmark simulation results show that the proposed approach has fast convergence speed and its measurement performance is almost identical to the crb

global existence of weak solution to compressible navier stokes allen cahn system in three dimensions abstract in this paper we construct a global weak solution to the compressible navier stokes allen cahn system with possibly large initial data the result holds in three dimensions subject to the conditions that the initial energy is finite and that the adiabatic constant 2

on the compactness of the reduced gravity two and a half layer equations abstract we consider the reduced gravity two and a half model in oceanic fluid dynamics and prove the stability of weak solutions in periodic domain t 2 the proof is based on the uniform a priori estimates and the method of weak convergence and the limit is carried out with the help of a new higher regularity estimate of the velocity which is derived by constructing a special test function

an em algorithm for ion channel current estimation parameter estimation of a continuous time markov chain observed through a discrete time memoryless channel is studied an expectation maximization em algorithm for maximum likelihood estimation of the parameter of this hidden markov process is developed and applied to a simple example of modeling ion channel currents in living cell membranes the approach follows that of asmussen nerman and olsson and ryden for em estimation of an underlying continuous time markov chain

explicit causal recursive estimators for continuous time bivariate markov chains a bivariate markov chain comprises a pair of random processes which are jointly markov in this paper both processes are assumed to be continuous time with finite state space one of the two processes is observable while the other is an underlying process which affects the statistical properties of the observable process neither the observable nor the underlying process is required to be a markov chain examples of bivariate markov chains include the markov modulated markov process mmmp the markov modulated poisson process mmpp and the batch markovian arrival process bmap we develop explicit causal recursions for estimating the number of jumps from one state to another and the total sojourn time in each state of a general bivariate markov chain explicit causal recursions of these statistics were previously developed for the mmmp and the mmpp using the transformation of measure approach we argue that this approach cannot be extended to a general bivariate markov chain instead we modify the approach developed by ryden for noncausal estimation of the same statistics of an mmpp and use the state augmentation approach of zeitouni and dembo and a matrix recursion from stiller and radons to derive the causal recursions the new recursions do not require any numerical integration or sampling scheme of the continuous time bivariate markov chain

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

the critical velocity for vortex existence in a two dimensional rotating bose einstein condensate we investigate a model corresponding to the experiments for a two dimensional rotating bose einstein condensate it consists in minimizing a gross pitaevskii functional defined in r 2 under the unit mass constraint we estimate the critical rotational speed 1 for vortex existence in the bulk of the condensate and we give some fundamental energy estimates for velocities close to 1

non existence of classical solutions with finite energy to the cauchy problem of the compressible navier stokes equations the well posedness of classical solutions with finite energy to the compressible navier stokes equations cns subject to arbitrarily large and smooth initial data is a challenging problem in the case when the fluid density is away from vacuum strictly positive this problem was first solved for the cns in either one dimension for general smooth initial data or multi dimension for smooth initial data near some equilibrium state that is small perturbation antontsev et al in boundary value problems in mechanics of nonhomogeneous fluids north holland publishing co amsterdam 1990 kazhikhov in sibirsk mat zh 23 60 64 1982 kazhikhov et al in prikl mat meh 41 282 291 1977 matsumura and nishida in proc jpn acad ser a math sci 55 337 342 1979 j math kyoto univ 20 67 104 1980 commun math phys 89 445 464 1983 in the case that the flow density may contain a vacuum the density can be zero at some space time point it seems to be a rather subtle problem to deal with the well posedness problem for cns the local well posedness of classical solutions containing a vacuum was shown in homogeneous sobolev space without the information of velocity in l2 norm for general regular initial data with some compatibility conditions being satisfied initially cho et al in j math pures appl 9 83 243 275 2004 cho and kim in j differ equ 228 377 411 2006 manuscr math 120 91 129 2006 choe and kim in j differ equ 190 504 523 2003 and the global existence of a classical solution in the same space is established under the additional assumption of small total initial energy but possible large oscillations huang et al in commun pure appl math 65 549 585 2012 however it was shown that any classical solutions to the compressible navier stokes equations in finite energy inhomogeneous sobolev space cannot exist globally in time since it may blow up in finite time provided that the density is compactly supported xin in commun pure appl math 51 229 240 1998 in this paper we investigate the well posedess of classical solutions to the cauchy problem of navier stokes equations and prove that the classical solution with finite energy does not exist in the inhomogeneous sobolev space for any short time under some natural assumptions on initial data near the vacuum this implies in particular that the homogeneous sobolev space is as crucial as studying the well posedness for the cauchy problem of compressible navier stokes equations in the presence of a vacuum at far fields even locally in time

convergence of the parabolic ginzburg landau equation to motion by mean curvature for the complex parabolic ginzburg landau equation we prove that asymptotically vorticity evolves according to motion by mean curvature in brakke s weak formulation the only assumption is a natural energy bound on the initial data in some cases we also prove convergence to enhanced motion in the sense of ilmanen