some remark on the existence of infinitely many nonphysical solutions to the incompressible navier stokes equations abstract we prove that there exist infinitely many distributional solutions with infinite kinetic energy to both the incompressible navier stokes equations in r 2 and burgers equation in r with vanishing initial data

on nonperiodic euler flows with holder regularity in isett regularity in time along the coarse scale flow for the euler equations 2013 the first author proposed a strengthening of onsager s conjecture on the failure of energy conservation for incompressible euler flows with holder regularity not exceeding 1 3 this stronger form of the conjecture implies that anomalous dissipation will fail for a generic euler flow with regularity below the onsager critical space l t infty b 3 infty 1 3 due to low regularity of the energy profile this paper is the first and main paper in a series of two the results of which may be viewed as first steps towards establishing the conjectured failure of energy regularity for generic solutions with holder exponent less than 1 5 the main result of the present paper shows that any given smooth euler flow can be perturbed in c 1 5 epsilon t x on any pre compact subset of mathbb r times mathbb r 3 to violate energy conservation furthermore the perturbed solution is no smoother than c 1 5 epsilon t x as a corollary of this theorem we show the existence of nonzero c 1 5 epsilon t x solutions to euler with compact space time support generalizing previous work of the first author isett holder continuous euler flows in three dimensions with compact support in time 2012 to the nonperiodic setting

regression analysis when covariates are regression parameters of a random effects model for observed longitudinal measurements summary we consider regression analysis when covariate variables are the underlying regression coefficients of another linear mixed model a naive approach is t o use each subject s repeated measurements which are assumed to follow a linear mixed model and obtain subject specific estimated coefficients to replace the covariate variables however directly replacing the unobserved covariates in the primary regression by these estimated coefficients may result in a significantly biased estimator the aforementioned problem can be evaluated as a generalization of the classical additive error model where repeated measures are considered as replicates to correct for these biases we investigate a pseudo expected estimating equation eee estimator a regression calibration rc estimator and a refined version of the rc estimator for linear regression the first two estimators are identical under certain conditions however when the primary regression model is a nonlinear model the rc estimator is usually biased we thus consider a refined regression calibration estimator whose performance is close to that of the pseudo eee estimator but does not require numerical integration the rc estimator is also extended to the proportional hazards regression model in addition to the distribution theory we evaluate the methods through simulation studies the methods are applied to analyze a real dataset from a child growth study

orthogonal polynomials and some q beta integrals of ramanujan abstract two integrals of ramanujan are used to define a q analogue of the euler beta integral on the real line and of the cauchy beta integral on the complex unit circle such integrals are connected to orthogonal biorthogonal and laurent polynomials explicit examples of laurent orthogonal polynomials are given on the real line and on the circle

zeros of orthogonal laurent polynomials and solutions of strong stieltjes moment problems the strong stieltjes moment problem for a bisequence c n n consists of finding positive measures m with support in 0 such that 0 t nd m t c nfor n 0 1 2 orthogonal laurent polynomials associated with the problem play a central role in the study of solutions when the problem is indeterminate the odd and even sequences of orthogonal laurent polynomials suitably normalized converge in c 0 to distinct holomorphic functions the zeros of each of these functions constitute together with the origin the support of two solutions m and m 0 we discuss how odd and even subsequences of zeros of the orthogonal laurent polynomials converge to the support points of m and m 0

robustness of one dimensional viscous fluid motion under multidimensional perturbations abstract we adapt the relative energy functional associated to the compressible navier stokes system to show stability of solutions emanating from 1 d initial data with respect to multidimensional n 2 3 perturbations besides the application of the relative energy inequality as a suitable distance between two solutions refined regularity estimates in l p based sobolev spaces are used

orthogonal laurent polynomials a new algebraic approach abstract in this paper some important algebraic aspects in the theory of orthogonal laurent polynomials such as the three term recurrence relation the christoffel darboux identity or the liouville ostrogradski formula are revisited from the riemann hilbert window these topics are considered for general ordered laurent polynomial sequences and not only for the usual balanced cases in addition a connection with szego polynomials orthogonal polynomials in the unit circle is explored

another quadrature rule of highest algebraic degree of precision we consider certain quadrature rules of highest algebraic degree of precision that involve strong stieltjes distributions i e strong distributions on the positive real axis the behavior of the parameters of these quadrature rules when the distributions are strong c inversive stieltjes distributions is given a quadrature rule whose parameters have explicit expressions for their determination is presented an application of this quadrature rule for the evaluation of a certain type of integrals is also given

global ill posedness of the isentropic system of gas dynamics we consider the isentropic compressible euler system in 2 space dimensions with pressure law p 2 and we show the existence of classical riemann data i e pure jump discontinuities across a line for which there are infinitely many admissible bounded weak solutions bounded away from the void we also show that some of these riemann data are generated by a 1 dimensional compression wave our theorem leads therefore to lipschitz initial data for which there are infinitely many global bounded admissible weak solutions c 2015 wiley periodicals inc

global well posedness issues for the inviscid boussinesq system with yudovich s type data the present paper is dedicated to the study of the global existence for the inviscid two dimensional boussinesq system we focus on finite energy data with bounded vorticity and we find out that under quite a natural additional assumption on the initial temperature there exists a global unique solution no smallness conditions are imposed on the data the global existence issues for infinite energy initial velocity and for the benard system are also discussed

orthogonal laurent polynomials and strong moment theory a survey these topics are found in many parts of 20th century mathematics and its applications in mathematical physics chemistry statistics and engineering historically the analytic theory of continued fractions has played a central role in both the origin and the development of the other topics continued fractions are intimately related to pad e approximants and special functions emphasis is given to the development of strong moment theory and orthogonal laurent polynomials and to the related continued fractions quadrature formulas integral transforms and linear functionals by a strong moment problem we mean the following for a given bisequence n n of real numbers does there exist a distribution function such that

general existence theorems for hamilton jacobi equations in the scalar and vectorial cases keywords dirichlet problem hamilton jacobi equation existence of solutions reference caa article 1997 002doi 10 1007 bf02392708view record in web of science record created on 2008 11 25 modified on 2017 05 12

on admissibility criteria for weak solutions of the euler equations we consider solutions to the cauchy problem for the incompressible euler equations satisfying several additional requirements like the global and local energy inequalities using some techniques introduced in an earlier paper we show that for some bounded compactly supported initial data none of these admissibility criteria singles out a unique weak solution as a byproduct in more than one space dimension we show bounded initial data for which admissible solutions to the p system of isentropic gas dynamics in eulerian coordinates are not unique

cocaine dependence treatment data methods for measurement error problems with predictors derived from stationary stochastic processes in a cocaine dependence treatment study we use linear and nonlinear regression models to model posttreatment cocaine craving scores and first cocaine relapse time a subset of the covariates are summary statistics derived from baseline daily cocaine use trajectories such as baseline cocaine use frequency and average daily use amount these summary statistics are subject to estimation error and can therefore cause biased estimators for the regression coefficients unlike classical measurement error problems the error we encounter here is heteroscedastic with an unknown distribution and there are no replicates for the error prone variables or instrumental variables we propose two robust methods to correct for the bias a computationally efficient method of moments based method for linear regression models and a subsampling extrapolation method that is generally applicable to both linear and nonlinear regression models simulations and an application to the cocaine dependence treatment data are used to

dissipative continuous euler flows we show the existence of continuous periodic solutions of the 3d incompressible euler equations which dissipate the total kinetic energy

joint modeling and clustering paired generalized longitudinal trajectories with application to cocaine abuse treatment data in a cocaine dependence treatment study we have paired binary longitudinal trajectories that record the cocaine use patterns of each patient before and after a treatment to better understand the drug using behaviors among the patients we propose a general framework based on functional data analysis to jointly model and cluster these paired non gaussian longitudinal trajectories our approach assumes that the response variables follow distributions from the exponential family with the canonical parameters determined by some latent gaussian processes to reduce the dimensionality of the latent processes we express them by a truncated karhunen loeve kl expansion allowing the mean and covariance functions to be different across clusters we further represent the mean and eigenfunctions functions by flexible spline bases and determine the orders of the truncated kl expansions using data driven methods by treating the cluster membership as a missing value we cluster the cocaine use trajectories by a l

conditional estimation for generalized linear models when covariates are subject specific parameters in a mixed model for longitudinal measurements the relationship between a primary endpoint and features of longitudinal profiles of a continuous response is often of interest and a relevant framework is that of a generalized linear model with covariates that are subject specific random effects in a linear mixed model for the longitudinal measurements naive implementation by imputing subject specific effects from individual regression fits yields biased inference and several methods for reducing this bias have been proposed these require a parametric normality assumption on the random effects which may be unrealistic adapting a strategy of stefanski and carroll 1987 biometrika74 703 716 we propose estimators for the generalized linear model parameters that require no assumptions on the random effects and yield consistent inference regardless of the true distribution the methods are illustrated via simulation and by application to a study of bone mineral density in women transitioning to menopause

a new proof of the caffarelli kohn nirenberg theorem here we give a self contained new proof of the partial regularity theorems for solutions of incompressible navier stokes equations in three spatial dimensions these results were originally due to scheffer and caffarelli kohn and nirenberg our proof is much more direct and simpler 1998 john wiley sons inc

dissipative euler flows with onsager critical spatial regularity for any 0 we show the existence of continuous periodic weak solutions v of the euler equations that do not conserve the kinetic energy and belong to the space lt1 cx1 3 e namely x v x t is e holder continuous in space at a e time t and the integral t 1 3 edt is finite a well known open conjecture of l onsager claims that such solutions exist even in the class lt cx1 3 e 2016 wiley periodicals inc

orthogonal laurent polynomials and continued fractions associated with log normal distributions abstract this paper describes properties and computational procedures related to orthogonal laurent polynomials continued fractions two point pade approximants strong moment problems and l gaussian quadrature associated with log normal distribution functions t defined by t q1 2 2 e lnt 2 2 0

compressible fluids driven by stochastic forcing the relative energy inequality and applications we show the relative energy inequality for the compressible navier stokes system driven by a stochastic forcing as a corollary we prove the weak strong uniqueness property pathwise and in law and convergence of weak solutions in the inviscid incompressible limit in particular we establish a yamada watanabe type result in the context of the compressible navier stokes system that is pathwise weak strong uniqueness implies weak strong uniqueness in law

joint models for a primary endpoint and multiple longitudinal covariate processes summary joint models are formulated to investigate the association between a primary endpoint and features of multiple longitudinal processes in particular the subject specific random effects in a multivariate linear random effects model for multiple longitudinal processes are predictors in a generalized linear model for primary endpoints li zhang and davidian 2004 biometrics60 1 7 proposed an estimation procedure that makes no distributional assumption on the random effects but assumes independent within subject measurement errors in the longitudinal covariate process based on an asymptotic bias analysis we found that their estimators can be biased when random effects do not fully explain the within subject correlations among longitudinal covariate measurements specifically the existing procedure is fairly sensitive to the independent measurement error assumption to overcome this limitation we propose new estimation procedures that require neither a distributional or covariance structural assumption on covariate random effects nor an independence assumption on within subject measurement errors these new procedures are more flexible readily cover scenarios that have multivariate longitudinal covariate processes and can be implemented using available software through simulations and an analysis of data from a hypertension study we evaluate and illustrate the numerical performances of the new estimators

localised relative energy and finite speed of propagation for compressible flows abstract for the incompressible and the isentropic compressible euler equations in arbitrary space dimension we establish the principle of localised relative energy thus generalising the well known relative energy method to this end we adapt classical arguments of c dafermos to the euler equations we give several applications to the behaviour of weak solutions like local weak strong uniqueness local preservation of smoothness and finite speed of propagation for the isentropic system

self similar 2d euler solutions with mixed sign vorticity we construct a class of self similar 2d incompressible euler solutions that have initial vorticity of mixed sign the boundaries between regions of positive and negative vorticity form algebraic spirals similar to the kaden spiral and as opposed to prandtl s logarithmic vortex spirals also unlike the prandtl case spirals are not initially present

global well posedness of strong solutions to the 3d primitive equations with horizontal eddy diffusivity in this paper we consider the initial boundary value problem of the 3d primitive equations for oceanic and atmospheric dynamics with only horizontal diffusion in the temperature equation global well posedness of strong solutions are established with h2 initial data 2014 elsevier inc all rights reserved

a possible counterexample to well posedness of entropy solutions and to godunov scheme convergence a particular case of initial data for the two dimensional euler equations is studied numerically the results show that the godunov method does not always converge to the physical solution at least not on feasible grids moreover they suggest that entropy solutions in the weak entropy inequality sense are not well posed

two point pade expansions for a family of analytic functions abstract each member g z of a family of analytic functions defined by stieltjes transforms is shown to be represented by a positive t fraction the approximants of which form the main diagonal in the two point pade table of g z the positive t fraction is shown to converge to g z throughout a domain d a b z z b a uniformly on compact subsets in addition truncation error bounds are given for the approximants of the continued function these bounds supplement previously known bounds and apply in part of the domain of g z not covered by other bounds the proofs of our results employ properties of orthogonal l polynomials laurent polynomials and l gaussian quadrature which are of some interest in themselves a number of examples are considered

non existence of strong regular reflections in self similar potential flow abstract we consider shock reflection which has a well known local non uniqueness the reflected shock can be either of two choices called weak and strong we consider cases where existence of a global solution with weak reflected shock has been proven for compressible potential flow if there was a global strong shock solution as well then potential flow would be ill posed however we prove non existence of strong shock analogues in a natural class of candidates

asymptotics for the simex estimator in nonlinear measurement error models abstract cook and stefanski have described a computer intensive method the simex method for approximately consistent estimation in regression problems with additive measurement error in this article we derive the asymptotic distribution of their estimators and show how to compute estimated standard errors these standard error estimators can either be used alone or as prepivoting devices in a bootstrap analysis we also give theoretical justification to some of the phenomena observed by cook and stefanski in their simulations

on a symmetry in strong distributions a strong stieltjes distribution d t is called symmetric if it satises the property t d 2 t 2 t d t for t 2 a b 0 1 2 2 z and 0 in this article some consequences of symmetry on the moments the orthogonal l polynomials and the quadrature formulae associated with the distribution are given c 1999 elsevier science b v all rights reserved msc 30e05 30b70 41a55

weak solutions with decreasing energy of incompressible euler equations weak solution of the euler equations is an l2 vector field u x t satisfying certain integral relations which express incompressibility and the momentum balance our conjecture is that some weak solutions are limits of solutions of viscous and compressible fluid equations as both viscosity and compressibility tend to zero thus we believe that weak solutions describe turbulent flows with very high reynolds numbers

on the nonuniqueness of weak solution of the euler equation weak solution of the euler equations is defined as an l2 vector field satisfying the integral relations expressing the mass and momentum balance their general nature has been quite unclear in this work an example of a weak solution on a 2 dimensional torus is constructed that is identically zero outside a finite time interval this example is simpler and more transparent than the previous example of v scheffer j geom anal 3 4 1993 pp 343 401 1997 john wiley sons inc

exponential time differencing for the tracer equations appearing in primitive equation ocean models abstract the tracer equations are part of the primitive equations used in ocean modeling and describe the transport of tracers such as temperature salinity or chemicals in the ocean depending on the number of tracers considered several equations may be added to and coupled to the dynamics system in many relevant situations the time step requirements of explicit methods imposed by the transport and mixing in the vertical direction are more restrictive than those for the horizontal and this may cause the need to use very small time steps if a fully explicit method is employed to overcome this issue we propose an exponential time differencing etd solver where the vertical terms transport and diffusion are treated with a matrix exponential whereas the horizontal terms are dealt with in an explicit way we investigate numerically the computational speed ups that can be obtained over other semi implicit methods and we analyze the advantages of the method in the case of multiple tracers

on the energy dissipation rate of solutions to the compressible isentropic euler system in this paper we extend and complement the results in chiodaroli et al global ill posedness of the isentropic system of gas dynamics 2014 on the well posedness issue for weak solutions of the compressible isentropic euler system in 2 space dimensions with pressure law p 1 first we show that every riemann problem whose one dimensional self similar solution consists of two shocks admits also infinitely many two dimensional admissible bounded weak solutions not containing vacuum generated by the method of de lellis and szekelyhidi ann math 170 1417 1436 2009 arch ration mech anal 195 225 260 2010 moreover we prove that for some of these riemann problems and for 1 3 such solutions have a greater energy dissipation rate than the self similar solution emanating from the same riemann data we therefore show that the maximal dissipation criterion proposed by dafermos in j diff equ 14 202 212 1973 does not favour the classical self similar solutions

finite time blowup for the inviscid primitive equations of oceanic and atmospheric dynamics in an earlier work we have shown the global for all initial data and all time well posedness of strong solutions to the three dimensional viscous primitive equations of large scale oceanic and atmospheric dynamics in this paper we show that for certain class of initial data the corresponding smooth solutions of the inviscid non viscous primitive equations if they exist they blow up in finite time specifically we consider the three dimensional inviscid primitive equations in a three dimensional infinite horizontal channel subject to periodic boundary conditions in the horizontal directions and with no normal flow boundary conditions on the solid top and bottom boundaries for certain class of initial data we reduce this system into the two dimensional system of primitive equations in an infinite horizontal strip with the same type of boundary conditions and then we show that for specific sub class of initial data the corresponding smooth solutions of the reduced inviscid two dimensional system develop singularities in finite time

counterexamples to the sonic criterion we consider self similar pseudo steady shock reflection at an oblique wall there are three parameters wall corner angle mach number angle of incident shock ever since ernst mach discovered the irregular reflection named after him researchers have sought to predict precisely for which parameters the reflection is regular three conflicting proposals the detachment sonic and von neumann criteria have been studied extensively without a clear result we demonstrate that the sonic criterion is not correct we consider polytropic potential flow and prove that there is an open nonempty set of parameters that admit a global regular reflection with a reflected shock that is transonic we also provide a clear physical reason the flow type sub or supersonic is not decisive instead the reflected shock type weak or strong determines whether structural perturbations decay towards the reflection point

length biasing and laws equivalent to the log normal abstract let x 0 denote a generic lifetime of a renewal process having unit mean lifetime let hat x denote the stationary total lifetime and let q 0 1 be a fixed constant we consider anew the scale invariance problem for which laws does q hat x have the same distribution as x our setting is more probabilistic than those presented hitherto and we explore connections with the log normal moment problem in particular it is shown that all explicitly known laws which have log normal moments solve our problem the notion of remaining lifetime is generalized and its scaling invariance is investigated using the notion of total lifetime two moment equivalent laws of askey are shown to have a simple representation in terms of laws equivalent to the log normal the representation involves a q gamma law which we explore in its own right an affine extension of our basic scale invariance relation arising in the theory of orthogonal polynomials is shown to be equivalent to the latter

h principles for the incompressible euler equations in dissipative euler flows and onsager s conjecture arxiv 1205 3626 preprint 2012 de lellis and szekelyhidi construct holder continuous dissipative weak solutions to the incompressible euler equations in the torus mathbb t 3 the construction consists of adding fast oscillations to the trivial solution we extend this result by establishing optimal h principles in two and three space dimensions specifically we identify all subsolutions defined in a suitable sense which can be approximated in the h 1 norm by exact solutions furthermore we prove that the flows thus constructed on mathbb t 3 are genuinely three dimensional and are not trivially obtained from solutions on mathbb t 2

orthogonal laurent polynomials and the strong hamburger moment problem abstract this paper is concerned with the strong hamburger moment problem shmp for a given double sequence of real numbers c c n does there exist a real valued bounded non decreasing function on with infinitely many points of increase such that for every integer n c n t n d t necessary and sufficient conditions for the existence of such a function are given in terms of the positivity of certain hankel determinants associated with c our approach is made through the study of orthogonal and quasi orthogonal laurent polynomials referred to here as l polynomials and closely related gaussian type quadrature formulas in the proof of sufficiency an inner product for l polynomials is defined in terms of the given double sequence c since orthogonal l polynomials are believed to be of interest in themselves some examples of specific systems are considered

spontaneous stochasticity and anomalous dissipation for burgers equation we develop a lagrangian approach to conservation law anomalies in weak solutions of inviscid burgers equation motivated by previous work on the kraichnan model of turbulent scalar advection we show that the entropy solutions of burgers possess markov stochastic processes of generalized lagrangian trajectories backward in time for which the burgers velocity is a backward martingale this property is shown to guarantee dissipativity of conservation law anomalies for general convex functions of the velocity the backward stochastic burgers flows with these properties are not unique however we construct infinitely many such stochastic flows both by a geometric construction and by the zero noise limit of the constantin iyer stochastic representation of viscous burgers solutions the latter proof yields the spontaneous stochasticity of lagrangian trajectories backward in time for burgers at unit prandtl number it is conjectured that existence of a backward stochastic flow with the velocity as martingale is an admissibility condition which selects the unique entropy solution for burgers we also study linear transport of passive densities and scalars by inviscid burgers flows we show that shock solutions of burgers exhibit spontaneous stochasticity backward in time for all finite prandtl numbers implying conservation law anomalies for linear transport we discuss the relation of our results for burgers with incompressible navier stokes turbulence especially lagrangian admissibility conditions for euler solutions and the relation between turbulent cascade directions and time asymmetry of lagrangian stochasticity

stability and spectral convergence of fourier method for nonlinear problems on the shortcomings of the 2 3 2 3 de aliasing method the high order accuracy of fourier method makes it the method of choice in many large scale simulations we discuss here the stability of fourier method for nonlinear evolution problems focusing on the two prototypical cases of the inviscid burgers equation and the multi dimensional incompressible euler equations the fourier method for such problems with quadratic nonlinearities comes in two main flavors one is the spectral fourier method the other is the 2 3 2 3 pseudo spectral fourier method where one removes the highest 1 3 1 3 portion of the spectrum this is often the method of choice to maintain the balance of quadratic energy and avoid aliasing errors two main themes are discussed in this paper first we prove that as long as the underlying exact solution has a minimal c 1 alpha c 1 spatial regularity then both the spectral and the 2 3 2 3 pseudo spectral fourier methods are stable consequently we prove their spectral convergence for smooth solutions of the inviscid burgers equation and the incompressible euler equations on the other hand we prove that after a critical time at which the underlying solution lacks sufficient smoothness then both the spectral and the 2 3 2 3 pseudo spectral fourier methods exhibit nonlinear instabilities which are realized through spurious oscillations in particular after shock formation in inviscid burgers equation the total variation of bounded pseudo spectral fourier solutions must increase with the number of increasing modes and we stipulate the analogous situation occurs with the 3d incompressible euler equations the limiting fourier solution is shown to enforce l 2 l 2 energy conservation and the contrast with energy dissipating onsager solutions is reflected through spurious oscillations

existence and non uniqueness of global weak solutions to inviscid primitive and boussinesq equations we consider the initial value problem for the inviscid primitive and boussinesq equations in three spatial dimensions we recast both systems as an abstract euler type system and apply the methods of convex integration of de lellis and szekelyhidi to show the existence of infinitely many global weak solutions of the studied equations for general initial data we also introduce an appropriate notion of dissipative solutions and show the existence of suitable initial data which generate infinitely many dissipative solutions

pc fractions and orthogonal laurent polynomials for log normal distributions abstract log normal distributions have received considerable recent attention partly through their applications to several branches of science economics and business and partly in their relation to orthogonal laurent polynomials l polynomials pade approximants and continued fractions this paper investigates pc fractions and orthogonal l polynomials associated with log normal distributions our main results include a explicit expressions for the continued fractions and their approximants and the l polynomials b proofs of the existence of the limits of subsequences of approximants and of l polynomials c closed form expressions for the limits of these subsequences and d identities between related approximants and related l polynomials several of the limit functions are seen to be essentially theta funcions

young measures generated by ideal incompressible fluid flows in their seminal paper diperna and majda commun math phys 108 4 667 689 1987 introduced the notion of a measure valued solution for the incompressible euler equations in order to capture complex phenomena present in limits of approximate solutions such as persistence of oscillation and development of concentrations furthermore they gave several explicit examples exhibiting such phenomena in this paper we show that any measure valued solution can be generated by a sequence of exact weak solutions in particular this gives rise to a very large arguably too large set of weak solutions of the incompressible euler equations

on self similar solutions to the incompressible euler equations abstract recent numerical simulations have shown the existence of multiple self similar solutions to the cauchy problem for the 2 dimensional incompressible euler equation with initial vorticity in l l o c p r 2 1 p toward a rigorous validation of these computations in this paper we analytically construct self similar solutions i on an outer domain of the form x r and ii in a neighborhood of the points where the solution exhibits a spiraling vortex singularity the outer solution is obtained as the fixed point of a contractive transformation based on the biot savart formula and integration along characteristics the inner solution is constructed using a system of adapted coordinates following the approach of v elling 2016 17

simulation extrapolation estimation in parametric measurement error models we describe a simulation based method of inference for parametric measurement error models in which the measurement error variance is known or at least well estimated the method entails adding add

global regularity for the 2d boussinesq equations with partial viscosity terms abstract in this paper we prove the global in time regularity for the 2d boussinesq system with either the zero diffusivity or the zero viscosity we also prove that as diffusivity viscosity tends to zero the solutions of the fully viscous equations converge strongly to those of zero diffusion viscosity equations our result for the zero diffusion system in particular solves the problem no 3 posed by moffatt in r l ricca ed kluwer academic publishers dordrecht the netherlands 2001 pp 3 10

fluids elasticity geometry and the existence of wrinkled solutions we are concerned with underlying connections between fluids elasticity isometric embedding of riemannian manifolds and the existence of wrinkled solutions of the associated nonlinear partial differential equations in this paper we develop such connections for the case of two spatial dimensions and demonstrate that the continuum mechanical equations can be mapped into a corresponding geometric framework and the inherent direct application of the theory of isometric embeddings and the gauss codazzi equations through examples for the euler equations for fluids and the euler lagrange equations for elastic solids these results show that the geometric theory provides an avenue for addressing the admissibility criteria for nonlinear conservation laws in continuum mechanics

the symmetric strong moment problem sequences of polynomials that occur as denominators in the two point pade table for two series expansions are considered in the special case when the series coefficients are solutions of a strong symmetric stieltjes moment problem the continued fractions whose convergents generate these polynomials as denominators are presented together with determinant representations for the polynomials and the continued fraction coefficients the log normal distribution is used as an example

the euler equations as a differential inclusion we propose a new point of view on weak solutions of the euler equations describing the motion of an ideal incompressible fluid in r n with n 2 we give a reformulation of the euler equations as a differential inclusion and in this way we obtain transparent proofs of several celebrated results of v scheffer and a shnirelman concerning the non uniqueness of weak solutions and the existence of energy decreasing solutions our results are stronger because they work in any dimension and yield bounded velocity and pressure