asymptotic behavior for the navier stokes equations with nonzero external forces abstract we estimate the asymptotic behavior for the stokes solutions with external forces first we found that if there are external forces then the energy decays slowly even if the forces decay quickly then we also obtain the asymptotic behavior in the temporal spatial direction for weak solutions of the navier stokes equations we also provide a simple example of external forces which shows that the stokes solution does not decay quickly

navier stokes flow in the weighted hardy space with applications to time decay problem abstract the asymptotic expansions of the navier stokes flow in r n and the rates of decay are studied with aid of weighted hardy spaces fujigaki and miyakawa 12 miyakawa 28 proved the nth order asymptotic expansion of the navier stokes flow if initial data decays like 1 x n 1 and if nth moment of initial data is finite in the present paper it is clarified that the moment condition for initial data is essential in order to obtain higher order asymptotic expansion of the flow and to consider the rapid time decay problem the second author 39 established the weighted estimates of the strong solutions in the weighted hardy spaces with small initial data which belongs to l n and a weighed hardy space firstly the refinement of the previous work 39 is achieved with alternative proof then the existence time of the solution in the weighted hardy spaces is characterized without any hardy norm as a result in two dimensional case the smallness condition on initial data is completely removed as an application the rapid time decay of the flow is investigated with aid of asymptotic expansions and of the symmetry conditions introduced by brandolese 3

asymptotic convergence rate of supercritical surface quasi geostrophic equation in morrey space abstract in this paper the asymptotic convergence rate of the supercritical surface quasi geostrophic equation in morrey space is investigated it is shown that if the global solution x t of the supercritical surface quasi geostrophic equation satisfies the growth condition in critical morrey space 0 t m p q r 2 r d t for r 2 p 2 p then every perturbed weak solution x t of the perturbed quasi geostrophic equation converges asymptotically to x t with the optimal rate t t l 2 o 1 t 1 as t in particular the initial perturbation is allowed large the findings are based on the spectral decomposition methods of fractional laplace and morrey space technique

solving group steiner problems as steiner problems abstract the generalized spanning tree or group steiner problem gsp is a generalization of the steiner problem in graphs spg one requires a tree spanning at least one vertex of each subset given in a family of vertex subsets while minimizing the sum of the corresponding edge costs specialized solution procedures have been developed for this problem in this paper we investigate the performance of a known but so far neglected transformation to the undirected steiner problem in graphs when combined with a recent metaheuristic for the spg this straightforward approach compares favorably with specialized gsp heuristics thus we set a standard for future algorithms

on the supnorm form of leray s problem for the incompressible navier stokes equations we show that t3 4 u t l r3 0 as t for all leray hopf s global weak solutions u t of the incompressible navier stokes equations in 3 it is also shown that t u t e tu0 l r3 0 as t where e t is the heat semigroup as well as other fundamental new results in spite of the complexity of the questions our approach is elementary and is based on standard tools like conventional fourier and energy methods

large time behavior for convection diffusion equations in rn abstract we describe the large time behavior of solutions of the convection diffusion equation u t u a u q 1 u in 0 r n with a r n and q 1 1 n n 1 when q 1 1 n we prove that the large time behavior of solutions with initial data in l 1 r n is given by a uniparametric family of self similar solutions the relevant parameter is the mass of the solution that is conserved for all t our result extends to dimensions n 1 well known results on the large time behavior of solutions for viscous burgers equations in one space dimension the proof is based on la salle s invariance principle applied to the equation written in its self similarity variables when q 1 1 n the convection term is too weak and the large time behavior is given by the heat kernel in this case the result is easily proved applying standard estimates of the heat kernel on the integral equation related to the problem

a note on lower bounds of decay rates for solutions to the navier stokes equations in the norms of besov spaces abstract we study the lower bounds of decay rates for turbulent solutions to the navier stokes equations in the norms of besov spaces we focus on solutions satisfying 0 lim inf t t u t lim sup t t u t for some 0 5 4 and prove among others that such solutions measured in the norm of the besov space b 2 2 are estimated for large times from below by some positive constant these estimates stem from sufficiently fast rate of large time energy concentration in low frequencies occurring in the studied solutions our results have simple proofs and improve and extend substantially the results published by miyakawa 2002 and by schonbek and wiegner 1996

global stability of large solutions to the 3d navier stokes equations we prove the stability of mildly decaying global strong solutions to the navier stokes equations in three space dimensions combined with previous results on the global existence of large solutions with various symmetries this gives the first global existence theorem for large solutions with approximately symmetric initial data the stability of unforced 2d flow under 3d perturbations is also obtained

lp stability for the strong solutions of the navier stokes equations in the whole space abstract we consider the motion of a viscous fluid filling the whole space r3 governed by the classical navier stokes equations 1 existence of global in time regular solutions for that system of non linear partial differential equations is still an open problem from either the mathematical and the physical point of view an interesting property is the stability or not of the eventual global regular solutions here we assume that v1 t x is a solution with initial data a1 x for small perturbations of a1 we want the solution v1 t x being slightly perturbed too due to viscosity it is even expected that the perturbed solution v2 t x approaches the unperturbed one as time goes to infinity this is just the result proved in this paper to measure the distance between v1 t x and v2 t x at each time t suitable norms are introduced lp norms for fluids filling a bounded vessel exponential decay of the above distance is expected such a strong result is not reasonable for fluids filling the entire space

chaotic synchronization cryptosystems combined with rsa encryption algorithm abstract chaotic synchronization has suffered from demodulating information by hackers via the public channel different methods have been developed to hide the contents of a message using chaotic signals nevertheless many studies have shown that most of the existing methods are unreliable in the aspect of security according to the above in order to enhance the strength of the cryptosystem and provide greater security we carry out double encryption which combines chaotic synchronization with rsa algorithm in this study a design methodology for neural network nn based secure communications in multiple time delay chaotic mtdc systems is proposed to obtain double encryption via rsa algorithm and chaotic synchronization rsa algorithm is an asymmetric encryption and its strength is based on the tremendous difficulty of factorizing two large prime numbers accordingly it takes much more time to process rsa algorithm if the length of the key is much longer a shorter key is used to decrease the processing time of rsa algorithm in this work nevertheless it will result in a lower security of the cryptosystem in order to enhance the strength of the cryptosystem we carry out double encryption which combines chaotic synchronization with rsa algorithm moreover an iga is proposed in this study to effectively overcome the weakness of the traditional ga on the basis of the iga a fuzzy controller is synthesized to not only realize the exponential synchronization but also achieve optimal h performance by minimizing the disturbances attenuation level finally a numerical example with simulations is given to illustrate the effectiveness of our approach

existence and temporal decay of regular solutions to non newtonian fluids combined with maxwell equations abstract we consider the cauchy problem of a certain type of non newtonian fluids combined with maxwell equations in three dimensions we establish local existence of unique regular solutions for sufficiently smooth initial data in addition the regular solutions are globally extended in time provided that the h 3 norm of the initial data is small enough lastly using the fourier splitting method we show that h l norms of the global regular solution decay with the rate of 1 t 3 4 l 2 for l 0 as time tends to infinity

l2 decay for the navier stokes flow in halfspaces on etudie le comportement asymptotique dans l 2 des solutions faibles des equations de navier stokes dans des demi espaces

asymptotic expansion for solutions of the navier stokes equations with potential forces abstract we derive an asymptotic expansion for smooth solutions of the navier stokes equations in weighted spaces this result removes previous restrictions on the number of terms of the asymptotics as well as on the range of the polynomial weights we also write the expansion in terms of expressions involving non linear quantities

on the asymptotic behaviour of the l 2 norm of suitable weak solutions to the navier stokes equations in three dimensional exterior domains we provel2 decay rates of suitable weak solutions to the navier stokes equations in exterior domains the results for the order of decay are the same as for the solutions to the cauchy problem of the navier stokes equations finally in the case of r3 the decay rate order is sharp in the class of solutions considered by us

large time decay and growth for solutions of a viscous boussinesq system in this paper we analyze the decay and the growth for large time of weak and strong solutions to the three dimensional viscous boussinesq system we show that generic solutions blow up as t in the sense that the energy and the l norms of the velocity field grow to infinity for large time for 1 p 3 in the case of strong solutions we provide sharp estimates both from above and from below and explicit asymptotic profiles we also show that solutions arising from u0 0 with zero mean for the initial temperature 0 have a special behavior as x or t tends to infinity contrarily to the generic case their energy dissipates to zero for large time

remark on the rate of decay of higher order derivatives for solutions to the navier stokes equations in rn we present a new derivation of upper bounds for the decay of higher order derivatives of solutions to the unforced navier stokes equations in rn the method based on so called gevrey estimates also yields explicit bounds on the growth of the radius of analyticity of the solution in time moreover under the assumption that the navier stokes solution stays sufficiently close to a solution of the heat equation in the l2 norm a result known to be true for a large class of initial data lower bounds on the decay of higher order derivatives can be obtained

space time asymptotics of the two dimensional navier stokes flow in the whole plane abstract we consider the space time behavior of the two dimensional navier stokes flow introducing some qualitative structure of initial data we succeed to derive the first order asymptotic expansion of the navier stokes flow without moment condition on initial data in l 1 r 2 l 2 r 2 moreover we characterize the necessary and sufficient condition for the rapid energy decay u t 2 o t 1 as t motivated by miyakawa schonbek 21 by weighted estimated in hardy spaces we discuss the possibility of the second order asymptotic expansion of the navier stokes flow assuming the first order moment condition on initial data moreover observing that the navier stokes flow u t lies in the hardy space h 1 r 2 for t 0 we consider the asymptotic expansions in terms of hardy norm finally we consider the rapid time decay u t 2 o t 3 2 as t with cyclic symmetry introduced by brandolese 2

on the weighted decay for solutions of the navier stokes system abstract we consider the question of to what extent the temporal decay u t l 2 o t 0 for solutions u of the navier stokes equation influences the decay of weighted norms we prove that x a u t l 2 o t 0 a 2 holds under the condition 0 a n 2 1 this extends the range of weights obtained in i kukavica j j torres weighted l p decay for solutions of the navier stokes equations commun partial differential equations 32 2007 819 831 a wider range of exponents is also obtained for the decay of l p norms

on upper and lower bounds of higher order derivatives for solutions to the 2d micropolar fluid equations the present paper is concerned with asymptotic behaviours of the solutions to the micropolar fluid motion equations in r2 upper and lower bounds are derived for the l2 decay rates of higher order derivatives of solutions to the micropolar fluid flows the findings are mainly based on the basic estimates of the linearized micropolar fluid motion equations and generalized gronwall type argument

energy decay for a weak solution of the navier stokes equation with slowly varying external forces we consider the navier stokes system with slowly decaying external forces formula we show that the energy norm of a weak solution has non uniform decay u t 2 0 t under suitable conditions on the data f and a which make the energy of solution bounded in time also we show the exact rate of the decay uniform decay of the energy u t 2 c 1 t e for external forces with a given explicit decay rate

temporal asymptotic behavior of solutions of the benjamin ono burgers equation abstract we study certain similarity solutions of the benjamin ono burgers bob equation and their role in the asymptotic behavior of the general solution for small initial data in l 1 r we prove that a solution of the bob equation exists in bc r l 1 r and depends continuously on its initial data results about existence uniqueness regularity and spatial asymptotics of solutions of a similarity reduction of the bob equation are proved furthermore the solutions of the bob equation are proved to converge as t to appropriate similarity solutions faster than the typically sharp rate of decay of the solutions

upper and lower bounds of temporal and spatial decays for the navier stokes equations we obtain the lower bounds of the temporal spatial decays for weak solutions of the navier stokes equations c0 1 t 5 2i4 1 2 i 2u t l2 c1 1 t 5 2i4 for i 1 2 the upper bound parts are estimated in several papers for example bae and jin submitted and he and xin proc roy soc edinburg section a 131 3 2001 597 by the interpolation arguments we also have c0 1 t 54 2 1 x 2 2u t l2 c1 1 t 54 2 for 0 2

asymptotic behavior of solutions to viscous conservation laws with slowly varying external forces this paper considers the existence and large time behavior of solutions to the convection diffusion equation ut u b x u u q 1 f x t in n 0 where f x t is slowly decaying and q 1 1 n or in some particular cases q 1 the initial condition u0 is supposed to be in an appropriate lp space uniform and nonuniform decay of the solutions will be established depending on the data and the forcing term

l 2 asymptotic stability of the mild solution to the 3d mhd equation in this paper we investigate the l 2 asymptotic stability of a global in time mild solution of the small initial value problem to the 3d magnetohydrodynamic mhd equations we construct a weak solution to the mhd equation and then we show this weak solution converges to the mild solution in the sense of l2 energy norm

lower bounds of rates of decay for solutions to the navier stokes equations where a p 3 2 p 1 and the constant c depends on the l2 and lnorms of the initial data u0 this paper deals with the more subtle problem of deriving lower bounds on the energy decay rates we show that for a certain class of initial data the solutions u x t to the 2d and 3d navier stokes equations admit an algebraic lower bound on the energy decay specifically there are two cases to consider in the first case the average of the initial data f u0 dx is nonzero this case was treated in the earlier paper 5 where it was established that

asymptotic behavior of weak solutions to the damped navier stokes equations abstract whether or not weak solutions of classical navier stokes equations decay to zero in l 2 as time tends to infinity was posed by leray in his pioneering paper 12 13 and has been well solved see 15 for instance this paper examines the three dimensional navier stokes equations with damping term u 1 u and proves that the weak solutions decay to zero in l 2 as time tends to infinity for any 1 by developing local in space estimate for weak solutions