existence and symmetries of solutions in besov morrey spaces for a semilinear heat wave type equation abstract this paper considers a semilinear integro differential equation of volterra type which interpolates semilinear heat and wave equations global existence of solutions is showed in spaces of besov type based in morrey spaces namely besov morrey spaces our initial data is larger than the previous works and our results provide a maximal existence class for semilinear interpolated heat wave equation some symmetries self similarity and asymptotic behavior of solutions are also investigated in the framework of besov morrey spaces

existence and large time behavior to coupled chemotaxis fluid equations in besov morrey spaces abstract the paper deals with the cauchy problem of coupled chemotaxis fluid equations by taking advantage of a coupling structure of the equations and using the semigroup approach we show existence and asymptotic stability with small initial data and external force u 0 n 0 c 0 c 0 n r 1 1 n r 2 2 n r 3 3 l m n for certain technical assumptions for the embedded relationship between function spaces we show that our initial data class is larger than that of kozono et al 2016 11 and covers physical cases of initial aggregation at points diracs and on filaments as an application we obtain a class of asymptotically existence of a basin of attraction for each self similar solutions with homogeneous initial data

design of variable structure controllers with continuous switching control a modified variable structure controller is proposed to deal with the conirol chattering problem which is one of the major difficulties for implementing the variable structure control vsc the new control strategy is effective for a class of uncertain nonlinear dynamical systems based on a suitably designed sliding sector a continuous switching controller whose control structure is switched whereas the control signal at switching remains continuous is constructed the complete attractiveness and the stability properties of the sliding sector in the sense of lyapunov stability ensure the retention of benefits achieved with the conventional vsc some typical examples are also investigated which show the improvement of system performance

a new design for model reference robust control using state space techniques the authors propose a model reference control mrc structure that is different from existing mrc structures the new approach that we discuss is based on state space techniques however it is not simply an alternative form of the input output transfer function approach the method we use to achieve our result is obtained through a concept often called filtered transformation the filtered transformation has the effect of transforming the plant into a big system that is composed of two subsystems one subsystem satisfies the standard matching condition which is not enjoyed by the original plant while all the unmatched and unmodelled dynamics are drawn into the other unmatched subsystem the control objective for the original plant is transferred into the control of the matched subsystem while also ensuring that the unmatched subsystem remains uniformly bounded a robust control approach and the backstepping method are used to guarantee that the overall states are globally uniformly bounded and that

combined direct and indirect approach to adaptive control an approach to adaptive control is introduced using a combination of both direct and indirect methods on the basis of estimates of the plant parameters and the current values of the control parameters closed loop estimation errors epsilon sub theta t and epsilon sub k t are defined these in turn are used in the adaptive laws for updating both identification and control parameters the global uniform stability of the overall system is shown by constructing a lyapunov function only the control of a first order plant is treated in detail to get across the principal concepts involved in particular the dynamic adjustment of the control parameters based on the estimates of the plant parameters is introduced as an indirect method and is the precursor of the combined method

local well posedness for a lotka volterra system in besov spaces this paper is devoted to study local existence uniqueness and continuous dependence upon the initial data of mild solutions for a diffusive non autonomous lotka volterra system initial data are taken in the besov space b p q n

variable structure model reference adaptive control using only input and output measurements abstract a variable structure model reference adaptive controller vs mrac using only the input and output measurements of the plant is proposed stability and transient properties are analysed and discussed remarkable transient behaviour is revealed in particular model following can be perfectly achieved in a finite time the effect of plant input disturbance is investigated and the performance of the vs controller is also shown to be qualitatively superior to that obtained with conventional integral adaptation algorithms a link between the vs mrac and the conventional mrac is suggested simulations are presented to highlight the theoretical results

a robust mrac using variable structure design for multivariable plants it is well known that undesirable transient responses and tracking performances have been frequently observed in traditional model reference adaptive control mrac problems especially for multivariable plants with unmodeled dynamics and output disturbances in this paper a new robust model reference adaptive control using variable structure design vsd is proposed to investigate the solution based on a definition of generalized relative degree grd for multivariable plants the general case for plants with arbitrary grd is completely solved it is shown that even when the uncertainties are presnet global stability and robustness of the closed loop control system are achieved furthermore without any persistence of excitation the tracking errors will at least asymptotically converge to zero for grd one plants and to a small residual set for plants with any higher grd with a suitable choice of initial control parameters the tracking errors can even be driven to zero in finite time for grd one plants and to a small residual set exponentially for plants with any higher grd

adaptive sliding mode control in discrete time systems abstract discrete time sliding mode control is considered the case of known parameters is first analyzed leading to a new definition of the so called equivalent control as the piecewise constant control that reduces to zero in finite time the distance of the system state from the sliding manifold in the presence of bounded parametric uncertainties an adaptive control scheme that guarantees the asymptotic satisfaction of the same control objective is presented the main feature of this approach is the reduction of the order of the relevant error equation and the possibility of dealing with the nonmatched uncertainties introduced by the sampling process

decomposition of hardy morrey spaces abstract in this paper we establish the decompositions of hardy morrey spaces in terms of atoms concentrated on dyadic cubes which have the same cancellation properties of the classical hardy spaces

semiclassical asymptotics gauge fields and quantum chaos a gauge field is given by a connection on a principal bundle p m we consider the semiclassical behavior of a family of schrodinger operators associated with a gauge field in the limit as h 0 we relate the spectral theory of such operators to behavior of the hamiltonian flow on the natural phase space associated to a gauge field examining in particular situations where this flow exhibits chaotic behavior

on the fuzzy initial value problem abstract the initial value problem x t f t x t x 0 x 0 with fuzzy initial value and with deterministic or fuzzy function f is considered two different approaches viz the extension principle and the use of extremal solutions of deterministic initial value problems are applied generalizations to fuzzy integral equations and fuzzy functional differential equations are indicated

on the stability of fuzzy dynamical systems abstract in this work we study the asymptotic behavior of fuzzy solutions obtained by using zadeh s extension at the deterministic solutions of initial value problems we obtain some result regarding the existence of fuzzy equilibrium points that generalize the already known results as show earlier the membership function of the fuzzy equilibrium points may be obtained in a relatively simple way also we study the projection of the fuzzy solution on the appropriate subspaces of the phase space several examples are given to illustrate the obtained results

morrey boundedness and compactness characterizations of integral commutators with singular kernel on strictly pseudoconvex domains in cn abstract we prove the morrey boundedness and compactness characterization of integral commutators with singular kernel of calderon zygmund type on pseudo convex domains in c n our results extend some of the ones of krantz li in 16 17

decompositions of besov morrey spaces and triebel lizorkin morrey spaces the aim of this paper is to define the besov morrey spaces and the triebel lizorkin morrey spaces and to present a decomposition of functions belonging to these spaces our results contain an answer to the conjecture proposed by mazzucato

robust model tracking control for a class of nonlinear plants we propose a new model following control scheme for a class of nonlinear plants the feedback control signal is a continuous function of all its arguments it is shown that this scheme guarantees that tracking error remains bounded and tends to a neighborhood of the origin with a rate not inferior to an exponential one furthermore it allows the designer to arbitrarily prescribe the rate of convergence and the size of the set of ultimate boundedness

identifier tracking model reference adaptive control model reference adaptive control is a major design method for controlling plants with uncertain parameters the primary objective of this paper is to develop a new design approach for a differentiator free model reference adaptive control of a single input single output linear time invariant plant the proposed method called the identifier tracking model reference adaptive control uses a stacked identifier structure that is new to the field of adaptive control the goal is to make the output of the plant asymptotically track the output of the first identifier and then driving the output of the first identifier to track that of the second identifier and so forth up to the qth identifier where q is the relative degree of the plant lastly the output of the qth identifier is forced to converge to that of the reference model simulation results show the superiority of the proposed method over the traditional model reference adaptive control with augmented error in terms of the transient response sinc

commutators of singular integrals and fractional integral operators the commutators of integral and differential operators are very important tools in harmonic analysis and pde recently the third author of this paper gave a survey front math china 2011 6 5 821 833 on some late results and put forward a few problems on commutators of many important operators in harmonic analysis in this paper we present some results about the commutators of singular integrals and fractional integrals with rough or variable kernels which can be seen as a supplement of the aforementioned survey

some remarks on the navier stokes equations in r3 we study various existence and uniqueness results for solutions of the navier stokes equations in connection with function spaces related to real harmonic analysis

global well posedness and asymptotic behavior in besov morrey spaces for chemotaxis navier stokes fluids in this work we consider the keller segel system coupled with navier stokes equations in rn for n 2 we prove the global well posedness with small initial data in besov morrey spaces our initial data class extends previous ones found in the literature such as that obtained by kozono miura and sugiyama j funct anal 270 5 1663 1683 2016 it allows us to consider initial cell density and fluid velocity concentrated on smooth curves or at points depending on the spatial dimension self similar solutions are obtained depending on the homogeneity of the initial data and considering the case of a chemical attractant without the degradation rate moreover we analyze the asymptotic stability of solutions at infinity and obtain a class of asymptotically self similar ones in this work we consider the keller segel system coupled with navier stokes equations in rn for n 2 we prove the global well posedness with small initial data in besov morrey spaces our initial data class extends previous ones found in the literature such as that obtained by kozono miura and sugiyama j funct anal 270 5 1663 1683 2016 it allows us to consider initial cell density and fluid velocity concentrated on smooth curves or at points depending on the spatial dimension self similar solutions are obtained depending on the homogeneity of the initial data and considering the case of a chemical attractant without the degradation rate moreover we analyze the asymptotic stability of solutions at infinity and obtain a class of asymptotically self similar ones

hausdorff besov type and triebel lizorkin type spaces and their applications abstract let s r p 1 and 0 1 p where p denotes the conjugate index of p in this article the authors first introduce the hausdorff besov type space b h p q s r n with q 1 and the hausdorff triebel lizorkin type space f h p q s r n with q 1 via a class of weights defined on the upper plane and then establish some equivalent characterizations of b h p q s r n and f h p q s r n via some classes of weights defined on r n the authors then prove that their dual spaces are besov morrey and triebel lizorkin morrey spaces respectively the relations between these spaces and the known besov triebel lizorkin hausdorff spaces are also studied as an application for p 1 and 0 n the authors obtain the coincidence between the space f h p 2 0 n n p r n and the predual space h p r n of the morrey space l p r n moreover characterizations of b h p q s r n and f h p q s r n via local means and peetre maximal functions as well as the boundedness of riesz potential operators and some singular integrals on b h p q s r n and f h p q s r n are also obtained

global strong solution to the semi linear keller segel system of parabolic parabolic type with small data in scale invariant spaces abstract we shall show existence of global strong solution to the semi linear keller segel system in r n n 3 of parabolic parabolic type with small initial data u 0 h n r 2 r r n and v 0 h n r r r n for max 1 n 4 r n 2 our method is based on the perturbation of linealization together with the l p l q estimates of the heat semigroup and the fractional powers of the laplace operator as a by product of our method we shall prove the decay property of solutions as the time goes to infinity

existence and uniqueness theorem on mild solutions to the keller segel system coupled with the navier stokes fluid abstract we consider the keller segel system coupled with the navier stokes fluid in the whole space and prove the existence of global mild solutions with the small initial data in the scaling invariant space our method is based on the implicit function theorem which yields necessarily continuous dependence of solutions for the initial data as a byproduct we show the asymptotic stability of solutions as the time goes to infinity since we may deal with the initial data in the weak l p spaces the existence of self similar solutions provided the initial data are small homogeneous functions

variable structure model reference adaptive control systems model reference adaptive controllers when only input and output measurements are available are designed using the theory of variable structure systems state variable filters are used in order to obtain differentiator free controllers the proposed design allows the error transient to be prescribed in advance the drawbacks deriving from the typical high frequency chattering of the control signal during the sliding motion can be partially eliminated by means of a little modification of the adaptation law that does not cause the error signal to deteriorate considerably

uniform global well posedness of the navier stokes coriolis system in a new critical space we prove global well posedness for the navier stokes coriolis system nsc in a critical space whose definition is based on fourier transform namely the fourier besov morrey space mathcal fn 1 mu infty mu 1 with 0 mu 3 the smallness condition on the initial data is uniform with respect to the angular velocity omega our result provides a new class for the uniform global solvability of nsc and covers some previous ones for mu 0 nsc is ill posedness in mathcal fn 1 mu infty mu 1 which shows the optimality of the results with respect to the space parameter mu 0 the lack of hausdorff young inequality in morrey spaces suggests that there are no inclusions between mathcal fn 1 mu infty mu 1 and the largest previously known existence classes of kozono yamazaki besov morrey space and koch tataru textit bmo 1 for navier stokes equations 3dns so taking in particular omega 0 we obtain a critical initial data class that seems to be new for global existence of solutions of 3dns

scaling in nonlinear parabolic equations the cauchy problem for parabolic equations with quadratic nonlinearity is studied we investigate the existence of global in time solutions and their large time behavior assuming some scaling property of the equation as well as of the norm of the banach space in which the solutions are constructed some applications of these abstract results are indicated

morrey regularity results for asymptotically convex variational problems with p q growth abstract we prove some global morrey regularity results for almost minimizers of functionals of the form u f x u d x this regularity is valid up to the boundary provided the boundary data is sufficiently regular the main assumption on f is that for each x the function f x behaves asymptotically like a convex function with p q growth some discontinuous behavior in the first argument is allowed as a main application we establish analogous regularity results for a broad class of systems of nonhomogeneous partial differential equations

gradient estimates below the duality exponent we show sharp local a priori estimates and regularity results for possibly degenerate non linear elliptic problems with data not lying in the natural dual space we provide a precise non linear potential theoretic analog of classical potential theory results due to adams duke math j 42 765 778 1975 and adams and lewis studia math 74 169 182 1982 concerning morrey spaces imbedding regularity properties for this we introduce a technique allowing for a non local representation of solutions via riesz potentials in turn yielding optimal local estimates simultaneously in both rearrangement and non rearrangement invariant function spaces in fact we also derive sharp estimates in lorentz spaces covering borderline cases which remained open for some while

a discrete transform and decompositions of distribution spaces abstract we study a representation formula of the form q q q for a distribution on r n this formula is obtained by discretizing and localizing a standard littlewood paley decomposition the map taking to the sequence q q with q running over the dyadic cubes in r n is called the transform the functions q and q have a particularly simple form moreover most of the familiar distribution spaces lp spaces 1 r n we also consider pointwise multipliers for the characteristic function of a domain we obtain boundedness results for a general class of domains which properly includes lipschitz domains several interpolation methods are easily analyzed via the sequence spaces for real interpolation we obtain among other things an extension to the case p 0 this in turn gives a new approach to the traditional atomic decomposition of hardy spaces

on the parameter convergence properties of a combined vs adaptive control scheme during sliding motion the effects of the use of a variable structure control component within an adaptive control scheme previously proposed by the authors 1992 1995 are investigated in this paper the discontinuous control action does not allow the explicit identification of the coefficients of the filters but only the identification of the so called equivalent control coinciding with the ideal control by coupling the variable structure control strategy with a continuous parameter adjustment mechanism it is instead possible to obtain an equivalent control which during the sliding motion turns out to be equal to a suitably constructed prediction error as long as the parameter adaptation is driven by both the tracking error which vanishes in finite time and the prediction error then the controller parameters prove to be exponentially convergent to the ideal values provided that the reference signal is sufficiently persistently exciting

well posedness for the navier stokes equations where u is the velocity and p is the pressure it is well known that the navierstokes equations are locally well posed for smooth enough initial data as long as one imposes appropriate boundary conditions on the pressure at for instance it is easy to see see 9 for much more general results that if s n 2 then for any h initial data there exists a unique c 0 t h r local solution with a pressure p c 0 t h r in the sequel we consider solutions for less regular initial data this has to be understood in the sense that the map from the initial data to the solution extends continuously to rougher function spaces the question we are interested in is the global well posedness for small data and local well posedness for large data with respect to a certain space of

a note on zadeh s extensions let f rn rn and f f rn f r n be zadeh s extension of f to the space of fuzzy compact sets f rn the aim of this paper is to show that if f is continuous then f f rn d f rn d is also continuous d being the supremum over hausdorff distances between their corresponding level sets

tracking with asymptotic sliding mode and adaptive input delay effect compensation of nonlinearly perturbed delayed systems applied to traffic feedback control abstractasymptotical sliding mode model reference adaptive control design for a class of systems with parametric uncertainty unknown nonlinear perturbation and external disturbance and with known input and state delays is proposed to overcome the difficulty to directly predict the plant state under uncertainties a control design is based on a developed decomposition procedure where a generalised error in conjunction with auxiliary linear dynamic blocks with adjustable gains is introduced and the sliding variable is formed on the basis of this error the effect of such a decomposition is to pull the input delay out of first step of the design procedure as a result similarly to the classical smith predictor the adaptive control architecture based only on the lumped delays i e without conventional in such cases difficult implemented distributed delay blocks two new adaptive control schemes are proposed a linearisation based control design is constructed for feedback control of an urban traffic

characterizations of morrey type besov and triebel lizorkin spaces with variable exponents abstract in this paper morrey type besov and triebel lizorkin spaces with variable exponents are introduced then equivalent quasi norms of these new spaces in terms of peetre s maximal functions are obtained finally applying those equivalent quasi norms the authors obtain the atomic molecular and wavelet decompositions of these new spaces

periodic orbits for fuzzy flows abstract periodic solutions are present in many of the various mathematical models that describe physical chemical or biological phenomena in this work we investigate the existence of periodic solutions for fuzzy initial value problem we will show that fuzzy solutions can present periodic points and we will develop tools of qualitative analysis for such solutions some models are presented to illustrate the results obtained in this paper

smoothness morrey spaces of regular distributions and some unboundedness property abstract we study smoothness spaces of morrey type on r n and characterise in detail when the spaces contain only regular distributions i e when they can be embedded into l 1 loc we also show that in all cases when it makes sense to study the growth envelope function of the proper smoothness morrey spaces it is always infinite

on the topological equivalence of some fuzzy flows near hyperbolic equilibria the purpose of this work is to study fuzzy dynamical systems associated with deterministic systems the grobman hartman theorem states that near hyperbolic equilibria there exists a homeomorphism between the nonlinear system s trajectories and the linearized correspondent system s trajectories that is these systems are topologically equivalent a theorem similar to grobman hartman theorem to fuzzy flows is the main result in this article for fuzzy flows obtained from each system it states that the nonlinear and the linearized are topologically equivalent

global well posedness for nonlocal fractional keller segel systems in critical besov spaces abstract in this paper we study keller segel systems with fractional diffusion and a nonlocal term we establish the global existence uniqueness and stability of solutions for systems with small initial data in critical besov spaces our main tools are the l p l q estimates for e t 2 in besov spaces and the perturbation of linearization

well posedness for the navier stokes equations with data in homogeneous sobolev lorentz spaces abstract in this paper we study local well posedness for the navier stokes equations nse with arbitrary initial data in homogeneous sobolev lorentz spaces h l q r s r d s 2 l q r for d 2 q 1 s 0 1 r and d q 1 s d q the obtained result improves the known ones for q d r q s 0 see cannone 1995 cannone and meyer 1995 for q r 2 d 2 1 s d 2 see cannone 1995 chemin 1992 and for s 0 d q 1 r see lemarie rieusset 2002 in the case of critical indexes s d q 1 we prove global well posedness for nse provided the norm of the initial value is small enough this result is also a generalization of the one in cannone 1997 and kozono and yamazaki 1995 27 meyer 1999 30 in which q r d s 0 and q d s 0 r respectively

adaptive backstepping controller design for stochastic jump systems in this technical note we improve the results in a paper by shi et al in which problems of stochastic stability and sliding mode control for a class of linear continuous time systems with stochastic jumps were considered however the system considered is switching stochastically between different subsystems the dynamics of the jump system can not stay on each sliding surface of subsystems forever therefore it is difficult to determine whether the closed loop system is stochastically stable in this technical note the backstepping techniques are adopted to overcome the problem in a paper by shi et al the resulting closed loop system is bounded in probability it has been shown that the adaptive control problem for the markovian jump systems is solvable if a set of coupled linear matrix inequalities lmis have solutions a numerical example is given to show the potential of the proposed techniques

fuzzy differential equations abstract this paper deals with fuzzy set valued mappings of a real variable whose values are normal convex upper semicontinuous and compactly supported fuzzy sets in rn we study differentiability and integrability properties of such functions and give an existence and uniqueness theorem for a solution to a fuzzy differential equation

a constructive proof of the fefferman stein decomposition of bmo rn let s vec r left left f r 1 f cdots r n f right f in h 1 left text r n text r right right subset h 1 left text r n text r n 1 right 22 1 begin gathered s vec r left vec g left g j right j 0 cdots n right in text bmo left text r n text r n 1 right sum limits j 0 n vec r j g j 0 text in bmo left text r n text r n 1 right left text r right end gathered 22 2 j 0

properties of min max controllers in uncertain dynamical systems we discuss properties of min max controllers previously obtained for uncertain dynamical systems in particular we present a new model for switching action and re examine asymptotic stability we demonstrate the attractiveness of switching surfaces and comment on the insensitivity of solutions in those surfaces to the uncertainty

besov morrey spaces function space theory and applications to non linear pde this paper is devoted to the analysis of function spaces modeled on besov spaces and their applications to non linear partial differential equations with emphasis on the incompressible isotropic navier stokes system and semilinear heat equations specifically we consider the class introduced by hideo kozono and masao yamazaki of besov spaces based on morrey spaces which we call besov morrey or bm spaces we obtain equivalent representations in terms of the weierstrass semigroup and wavelets and various embeddings in classical spaces we then establish pseudo differential and para differential estimates our results cover non regular and exotic symbols although the heat semigroup is not strongly continuous on morrey spaces we show that its action defines an equivalent norm in particular homogeneous bm spaces belong to a larger class constructed by grzegorz karch to analyze scaling in parabolic equations we compare karch s results with those of kozono and yamazaki and generalize them by obtaining short time existence and uniqueness of solutions for arbitrary data with subcritical regularity we exploit pseudo differential calculus to extend the analysis to compact smooth boundaryless riemannian manifolds bm spaces are defined by means of partitions of unity and coordinate patches and intrinsically in terms of functions of the laplace operator

well posedness for the navier stokes equations with datum in sobolev fourier lorentz spaces abstract in this note for s r and 1 p r we introduce and study sobolev fourier lorentz spaces h l p r s r d in the family spaces h l p r s r d the critical invariant spaces for the navier stokes equations correspond to the value s d p 1 when the initial datum belongs to the critical spaces h l p r d p 1 r d with d 2 1 p and 1 r we establish the existence of local mild solutions to the cauchy problem for the navier stokes equations in spaces l 0 t h l p r d p 1 r d with arbitrary initial value and existence of global mild solutions in spaces l 0 h l p r d p 1 r d when the norm of the initial value in the besov spaces b l p d p 1 r d is small enough where p may take some suitable values

some remarks on fuzzy differential equations via differential inclusions abstract in this paper we discuss the formulation and procedure for solving fuzzy differential equations via differential inclusions we give several examples showing the correct and incorrect procedure for solving fuzzy differential equations we show the connection between fuzzy differential equations and fuzzy differential inclusions finally we give some remarks on numerical algorithms for solving fuzzy differential equations via differential inclusions

dynamics and bifurcations of fuzzy nonlinear dynamical systems this article presents a study on how changes in fuzzy parameters can affect the behavior of fuzzy solutions such fuzzy solutions are obtained by applying the zadeh extension principle on deterministic solutions of autonomous differential equations we define the concepts of topological equivalence and fuzzy bifurcation value for fuzzy flows using these notions we prove some results for the existence of such bifurcation values we also provide some examples and computational simulations to illustrate the results

a combined direct indirect and variable structure method for robust adaptive control direct methods and indirect methods for the adaptive control of linear plants with unknown parameters are currently well known methods for combining direct and indirect methods have also been suggested in the paper the latter method is combined with the variable structure method new adaptive laws are suggested which overcome the principal drawbacks of the variable structure method while the direct and indirect components of the new method assure stability the variable structure component improves the transient response of the system simulation results are presented to show that the overall system is asymptotically stable in the ideal case and exhibits robustness and improved performance in the presence of perturbations

littlewood paley characterizations of triebel lizorkin morrey spaces via ball averages abstract let 1 p u and q 1 in this article the authors establish equivalent characterizations of the triebel lizorkin morrey space e u q p r n with smoothness order 0 2 in terms of the lusin area function and the g function generated by the difference between f x and its ball average b 2 j f x 1 b x 2 j b x 2 j f y d y j 1 2 x r n where for any j 1 2 and x r n b x 2 j y r n y x 2 j as applications the authors obtain several characterizations of e u p r n via pointwise inequalities involving ball averages

global existence and decay properties for a degenerate keller segel model with a power factor in drift term abstract the following degenerate parabolic system modelling chemotaxis is considered ks u t u m u q 1 v x r n t 0 v t v v u x r n t 0 u x 0 u 0 x v x 0 v 0 x x r n where m 1 q 2 0 or 1 and n 1 the aim of this paper is to prove the existence of a time global weak solution u v of ks with the l 0 l r n bound such a global bound is obtained in the case of i m q 2 n for large initial data and ii 1 m q 2 n for small initial data in the case of ii the decay properties of the solution u v are also discussed

the stationary navier stokes system in nonsmooth manifolds the poisson problem in lipschitz and c 1 domains we consider the linearized version of the stationary navier stokes equations on a subdomain of a smooth compact riemannian manifold m the emphasis is on regularity the boundary of is assumed to be only c1 and even lipschitz and the data are selected from appropriate sobolev besov scales our approach relies on the method of boundary integral equations suitably adapted to the variable coefficient setting we are considering here applications to the stationary nonlinear navier stokes equations in this context are also discussed

combined adaptive and variable structure control for constrained robots abstract this paper addresses the problem of controller design for constrained robots a control algorithm described as a combination of the direct adaptive and the variable structure method is presented for the trajectory tracking of an end effector on a constrained surface with specified constraint forces this scheme has certain advantages both with respect to computational efficiency and with respect to design with respect to computational efficiency the calculation of the regressor is avoided with respect to design since the number of parameter update laws required in the adaptation is independent of the number of links of the robot the difficulty of tuning numerous adaptation gains is avoided

fuzzy random variables abstract in this paper we define the concepts of fuzzy random variable and the expectation of a fuzzy random variable the new definition of expectation generalizes the integral of a set valued function we derive some properties of these new concepts by considering a suitable generalization of the hausdorff metric we derive the lebesgue dominated convergence type theorem

global existence result for chemotaxis navier stokes equations in the critical besov spaces abstract we consider the chemotaxis navier stokes equations which are the keller segel model coupled to the incompressible navier stokes equations in dimension three we prove the global existence of the solution in the critical besov spaces with small initial data only which is a new result and improves the previous result