existence results for the flow of viscoelastic fluids with a differential constitutive law where 2 is the symmetric extra stress tensor the total stress is given by g pl i where p is the hydrodynamic pressure 4 is the rate of deformation tensor g u vu vu u being the velocity field a is the relaxation time a2 the retardation time 0 i a a1 and q is the fluid viscosity the symbol a d t denotes an objective frame indifferent derivative i 181 more precisely

global well posedness of viscoelastic fluids of oldroyd type in besov spaces abstract we investigate a system of equations concerning an incompressible viscoelastic fluid of the oldroyd type which describes one class of non newtonian fluid with memory making use of a regularization method in conjunction with bony s paraproduct decomposition we obtain the existence and uniqueness of a small global solution for the above system in the besov spaces b 2 s with s d 2 and which implies global well posedness for small data in h s with s d 2 since the sobolev space h s is embedded in b 2 s

on the asymptotic distribution of exponentially weighted prediction error estimators the authors establish the distribution of the exponentially weighted prediction error estimators for a class of general possibly nonlinear discrete time systems an explicit formula for the covariance matrix of the estimation errors is provided the distributional results presented hold for a large number n of data points and a weighting or forgetting factor lambda close to one

incompressible limit of oldroyd b fluids in the whole space abstract this paper is dedicated to the study of compressible oldroyd b model in the framework of critical spaces we first prove the local well posedness for the compressible oldroyd b model with initial data 0 1 u 0 0 b 2 1 d 2 b 2 1 d 2 1 d b 2 1 d 2 d d the global well posedness is also established provided the initial data and coupling constant are sufficiently small on the basis of this we also consider the incompressible limit problem for ill prepared initial data we prove that as the mach number tends to zero the global solution to the compressible oldroyd b fluids converges to the solution to the corresponding incompressible model in some function spaces in the meanwhile the converge rates are obtained in some sense to fulfill our proof we give a new commutator estimate

global well posedness and decay rates for the three dimensional compressible oldroyd b model abstract in this paper we are concerned with the global well posedness and decay rates of strong solutions for the three dimensional compressible oldroyd b model we prove that this set of equations admits a unique global strong solution provided the initial data are close to the constant equilibrium state in h 2 framework moreover if the initial data belong to l 1 the convergence rate of the solutions in l p norm with 2 p 6 and convergence rates of their spatial derivatives in l 2 norm are obtained it is noteworthy that the smallness restriction on the coupling constant is not necessary in this paper

regularity results for the 2d critical oldroyd b model in the corotational case this paper studies the regularity results of classical solutions to the two dimensional critical oldroyd b model in the corotational case the critical case refers to the full laplacian dissipation in the velocity or the full laplacian dissipation in the non newtonian part of the stress tensor whether or not their classical solutions develop finite time singularities is a difficult problem and remains open the object of this paper is two fold firstly we establish the global regularity result to the case when the critical case occurs in the velocity and a logarithmic dissipation occurs in the non newtonian part of the stress tensor secondly when the critical case occurs in the non newtonian part of the stress tensor we first present many interesting global a priori bounds then establish a conditional global regularity in terms of the non newtonian part of the stress tensor this criterion comes naturally from our approach to obtain a global l bound for the vorticity

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

recursive least squares ladder estimation algorithms recursive least squares ladder estimation algorithms have attracted much attention recently because of their excellent convergence behavior and fast parameter tracking capability compared to gradient based algorithms we present some recently developed square root normalized exact least squares ladder form algorithms that have fewer storage requirements and lower computational requirements than the unnormalized ones a hilbert space approach to the derivations of magnitude normalized signal and gain recursions is presented the normalized forms are expected to have even better numerical properties than the unnormalized versions other normalized forms such as joint process estimators e g adaptive line enhancer and arma pole zero models will also be presented applications of these algorithms to fast or zero startup equalizers adaptive noise and echo cancellers non gaussian event detectors and inverse models for control problems are also mentioned

square root covariance ladder algorithms square root normalized ladder algorithms provide an efficient recursive solution to the problem of multichannel autoregressive model fitting a simplified derivation of the general update formulas for such ladder forms is presented and is used to develop the growing memory and sliding memory covariance ladder algorithms new ladder form realizations for the identified models are presented leading to convenient methods for computing the model parameters from estimated reflection coefficients a complete solution to the problem of possible singularity in the ladder update equations is also presented

on the control of viscoelastic jeffreys fluids abstract this paper is devoted to analyzing the control of vicoelastic fluids of the jeffreys kind also known as oldroyd models we will present the interesting problems with special emphasis in the difficulties that they involve then we will consider appropriate linear approximations and we will establish some partial approximate finite dimensional controllability results in an arbitrarily small time with distributed or boundary controls supported by arbitrarily small sets the proofs rely on some specific unique continuation properties which are implied by the structure of the solutions

global small solutions of 3d incompressible oldroyd b model without damping mechanism abstract in this paper we prove the global existence of small smooth solutions to the three dimensional incompressible oldroyd b model without damping on the stress tensor the main difficulty is the lack of full dissipation in stress tensor to overcome it we construct some time weighted energies based on the special coupled structure of system such type energies show the partial dissipation of stress tensor and the strongly full dissipation of velocity in the view of treating nonlinear term as a linear term we also apply this result to 3d incompressible viscoelastic system with hookean elasticity and then prove the global existence of small solutions without the physical assumption div curl structure as previous works

efficient algorithms for adaptive capon and apes spectral estimation in this paper fast algorithms for adaptive capon and amplitude and phase estimation apes methods for spectral analysis of time varying signals are derived fast stable nonrecursive formulae are derived based on time shifting properties of the pertinent variables as a consequence efficient frequency domain recursive least squares rls based as well as fast rls based algorithms for the adaptive estimation of the power spectra are developed stability issues of the frequency domain estimators are considered and stabilization procedures are proposed the computational complexity of the proposed algorithms is lower than relevant existing methods the performance of the proposed algorithms is demonstrated through extensive simulations

global solution to the incompressible oldroyd b model in the critical l p framework the case of the non small coupling parameter this paper is dedicated to the global well posedness issue of the incompressible oldroyd b model in the whole space mathbb r d with d geqq 2 it is shown that this set of equations admits a unique global solution in a certain critical lp type besov space provided that the initial data but not necessarily the coupling parameter is small enough as a consequence even through the coupling effect between the equations of velocity u and the symmetric tensor of constrains is not small one may construct the unique global solution to the oldroyd b model for a class of large highly oscillating initial velocity the proof relies on the estimates of the linearized systems of u and u mathbb p rm div tau which may be of interest for future works this result extends the work by chemin and masmoudi siam j math anal 33 84 112 2001 to the non small coupling parameter case

tracking improvements in fast rls algorithms using a variable forgetting factor the concept of a variable forgetting factor vff is incorporated into fast recursive least squares frls algorithms compromises in the data matrix that are needed to do this are examined both prewindowed and growing memory covariance algorithms are presented in transversal and lattice structures forgetting factor adaptation schemes which improve tracking performance over conventional frls algorithms are suggested finally the bias introduced by the use of the vff is analyzed

second order equivalence of rectangular and exponential windows in least squares estimation of gaussian autoregressive processes exact least squares algorithms for autoregressive signals can be made to track time varying parameters by using sliding windows on the data two common choices for such windows are the exponential one and the rectangular one in this paper it is shown that for gaussian autoregressive processes the two types of windows yield approximately the same mean square error if the windows parameters are properly chosen

global regularity of the high dimensional oldroyd b model in the corotational case abstract in this study we consider the global regularity of the high dimensional incompressible oldroyd b model in the corotational case with fractional dissipation u in particular under the assumption that 1 2 n 4 we determine the global regularity of the corresponding model