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

global regular and singular solutions for a model of gravitating particles the existence of solutions of a nonlinear parabolic equation describing the gravitational interaction of particles is studied for the initial data in spaces of generalized pseudomeasures this approach permits us to relax regularity assumptions on the initial conditions and to prove asymptotic stability results for the above problem

moment maps at the quantum level we introduce the notion of moment maps for quantum groups acting on their module algebras when the module algebras are quantizations of poisson manifolds we prove that the construction at the quantum level is a quantization of that at the semi classical level we also prove that the corresponding smashed product algebras are quantizations of the semi direct product poisson structures

global classical solutions in chemotaxis navier stokes system with rotational flux term the coupled chemotaxis fluid system nt n ns x n c c u n x t 0 t ct c nc u c x t 0 t ut u u u p n x t 0 t u 0 x t 0 t is considered under the no flux boundary conditions for n c and the dirichlet boundary condition for u on a bounded smooth domain rn n 2 3 0 1 we assume that s x n c is a matrix valued sensitivity under a mild assumption such that s x n c s0 c0 with some non decreasing function s0 c2 0 it contrasts with the related scalar sensitivity case that does not possess the natural gradient like functional structure associated estimates based on the natural functional seem no longer available in the present work a global classical solution is constructed under a smallness assumption on c0 l and moreover we obtain boundedness and large time convergence for the solution meaning that small initial concentration of chemical forces stabilization

quantized lax equations and their solutions integrable systems on quantum groups are investigated the heisenberg equations possessing the lax form are solved in terms of the solution to the factorization problem on the corresponding quantum group

on the general consensus protocol of multi agent systems with double integrator dynamics in this paper a general consensus protocol is considered for multi agent systems with double integrator dynamics the advantage of this protocol is that different consensus dynamics including linear periodic and positive exponential dynamics can be realized by choosing different gains necessary and sufficient conditions for solving the consensus problem with the considered general protocol are obtained namely all the gains realizing the consensus can be described the design method of the consensus protocol is constructively given moreover a periodic consensus protocol is obtained as a special case and it is revealed that the maximum convergence speed can be achieved by choosing suitable gains

a consensus algorithm in cat 0 space and its application to distributed fusion of phylogenetic trees abstract based on convex analysis a novel consensus algorithm of dynamical points in a cat 0 space is developed in this paper in which the associated communication graph uniformly contains a directed spanning tree the proposed algorithm provides an efficient method of solving consensus problems in a general cat 0 space while having certain robustness against weak communication the application of the new algorithm to the distributed fusion of phylogenetic trees is shown with demonstrative case simulations together with a study on the algorithm s robustness and efficiency

consensus on complete riemannian manifolds in finite time abstract in view of the fact that prototypes of riemannian manifolds range from euclidean surfaces to lie groups operator spaces etc the paper explores common consensus schemes for connected complete riemannian manifolds after studying the restriction exponential map we introduce a local consensus protocol with switching communication topologies for the manifolds via the isometric mapping based on one of the euclidean consensus protocols equipped with the compression decompression functions we extend the local consensus protocol and put forth a global consensus algorithm for any such manifolds these consensus schemes can provide common solutions to the consensus problems arising from various nonlinear spaces or abstract spaces belonging to connected complete riemannian manifolds in particular they are simple and concise and can converge in finite time simulation on the unit sphere is provided to verify our consensus schemes and to demonstrate the usage of our proposed techniques

global existence and boundedness in a keller segel stokes system involving a tensor valued sensitivity with saturation the 3d case abstract in this paper we continue to deal with the initial boundary value problem for the coupled keller segel stokes system n t u n n n s x n c c x t 0 t c t u c c c n x t 0 t u t p u n x t 0 t u 0 x t 0 t where r d is a bounded domain with smooth boundary and the chemotactic sensitivity s is not a scalar function but rather attains values in r d d and satisfies s x n c c s 1 n with some c s 0 and 0 when d 2 our previous work j differential equations 2015 has established the existence of global bounded classical solutions under the subcritical assumption 0 which is consistent with the corresponding results of the fluid free system but the method seems to be invalid in the three dimensional setting in this paper for the case d 3 we develop a new method to establish the existence and boundedness of global classical solutions for arbitrarily large initial data under the assumption 1 2 which is slightly stronger than the corresponding subcritical assumption 1 3 on the fluid free system where such an assumption is essentially necessary and sufficient for the existence of global bounded solutions the key idea here is to establish the general l p regularity of u from a rather low l p regularity of n which will be obtained by a new combinational functional

finite time weighted average consensus with respect to a monotonic function and its application abstract the consensus state is an important and fundamental quantity for consensus problems of multi agent systems which indicates where all the dynamical agents reach in this paper weighted average consensus with respect to a monotonic function which means that the trajectories of the monotonic function along the state of each agent reach the weighted average of their initial values is studied for a group of kinematic agents with time varying topology by constructing a continuous nonlinear distributed protocol such a consensus problem can be solved in finite time even though the time varying topology involves unconnected graphs then the distributed protocol is employed to compute the maximum likelihood estimation of unknown parameters over sensor networks compared with the existing results the estimate scheme proposed here may reduce the costs of data communication storage memory book keeping and computational overheads

technical communique sufficient conditions for the convergence of a class of nonlinear distributed consensus algorithms this paper is concerned with the convergence of a class of continuous time nonlinear consensus algorithms for single integrator agents in the consensus algorithms studied here the control input of each agent is assumed to be a state dependent combination of the relative positions of its neighbors in the information flow graph using a novel approach based on the smallest order of the nonzero derivative it is shown that under some mild conditions the convex hull of the agents has a contracting property a set valued lasalle like approach is subsequently employed to show the convergence of the agents to a common point the results are shown to be more general than the ones reported in the literature in some cases an illustrative example demonstrates how the proposed convergence conditions can be verified

the small convection limit in a two dimensional chemotaxis navier stokes system this paper deals with an initial boundary value problem for the chemotaxis navier stokes system begin aligned left begin array lcll n t u cdot nabla n delta n nabla cdot n nabla c qquad quad x in omega t 0 c t u cdot nabla c delta c nc qquad quad x in omega t 0 u t kappa u cdot nabla u delta u nabla p n nabla phi qquad quad x in omega t 0 nabla cdot u 0 qquad quad x in omega t 0 end array right end aligned in a bounded convex domain omega subset mathbb r 2 with smooth boundary with kappa in mathbb r and a given smooth potential phi omega rightarrow mathbb r it is known that for each kappa in mathbb r and all sufficiently smooth initial data this problem possesses a unique global classical solution n kappa c kappa u kappa the present work asserts that these solutions stabilize to n 0 c 0 u 0 uniformly with respect to the time variable more precisely it is shown that there exist mu 0 and c 0 such that whenever kappa in 1 1 begin aligned big vert n kappa cdot t n 0 cdot t big vert l infty omega big vert c kappa cdot t c 0 cdot t big vert l infty omega quad big vert u kappa cdot t u 0 cdot t big vert l infty omega le c kappa e mu t end aligned for all t 0 this result thereby provides an example for a rigorous quantification of stability properties in the stokes limit process as frequently considered in the literature on chemotaxis fluid systems in application contexts involving low reynolds numbers

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

symmetrization techniques on unbounded domains application to a chemotaxis system on rn the authors study the parabolic elliptic system on rn u t u u v 0 v v u u 0 u0 a version of the mathematical model of chemotaxis proposed by keller and segel a differential inequality for the quantity s0u t d where u is the decreasing rearrangement of the solution u t with respect to the spatial variable is obtained as a consequence they obtain e g lp bounds of the solution u v on r2 and global in time existence of solutions under the condition r2u0 8 then the solution u v blows up in a finite time compared to the previous work of diaz diaz and nagai adv math sci appl 5 1995 no 2 659 680 mr1361010 96j 35246 where this problem has been considered on bounded domains of rn there are some additional technical difficulties connected with the regularity of the derivative u t

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

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

global existence and asymptotic stability of the fractional chemotaxis fluid system in r3 abstract in this paper we consider a model arising from biology consisting of fractional chemotaxis equations coupled to viscous incompressible fluid equations throughout transport and external force in r 3 we establish the existence and uniqueness of global solution with small initial data by combining the local existence and a priori estimates as well as continuation argument moreover the decay rates of the solutions and their higher order spatial derivatives are established towards the equilibrium by introducing the negative sobolev space h s 0 s 3 2

generalized gel fand invariants and characteristic identities for quantum groups the generalized gel fand invariants for an arbitrary quantum group are explicitly constructed and their eigenvalues in any irreducible representation are computed these invariants enable one to develop characteristic identities for the quantum group and as a natural application these identities are used to construct projection operators for tensor products of representations to illustrate the general theory the quantum group uq gl m is studied in detail

global stability of homogeneous steady states in scaling invariant spaces for a keller segel navier stokes system abstract in this paper we study the global stability of homogeneous equilibria in keller segel navier stokes equations in scaling invariant spaces we prove that for any given 0 m 1 1 with 1 being the first eigenvalue of neumann laplacian the initial boundary value problem of the keller segel navier stokes system has a unique globally bounded classical solution provided that the initial datum is chosen sufficiently close to m m 0 in the norm of l d 2 w 1 d l d and satisfies a natural average mass condition our proof is based on the perturbation theory of semigroups and certain delicate exponential decay estimates for the linearized semigroup our result suggests a new observation that nontrivial classical solution for keller segel navier stokes equation can be obtained globally starting from suitable initial data with arbitrarily large total mass provided that volume of the bounded domain is large correspondingly

how to find the lax pair from the yang baxter equation we show explicitly how to construct the quantum lax pair from the yang baxter equation we demonstrate the new method by applying it to the heisenberg xyz model

on fock space representations of quantized enveloping algebras related to noncommutative differential geometry in this paper explicitly natural from the geometrical point of view fock space representations contragradient verma modules of the quantized enveloping algebras are constructed in order to do so one starts from the gauss decomposition of the quantum group and introduces the differential operators on the corresponding q deformed flag manifold assumed as a left comodule for the quantum group by a projection to it of the right action of the quantized enveloping algebra on the quantum group finally the representatives of the elements of the quantized enveloping algebra corresponding to the left invariant vector fields on the quantum group are expressed as first order differential operators on the q deformed flag manifold

global existence and convergence rates to a chemotaxis fluids system with mixed boundary conditions abstract in this paper we investigate the large time behavior of strong solutions to a chemotaxis fluids system in an unbounded domain with mixed boundary conditions based on the anisotropic l p technique the elliptic estimates and stokes estimates we first establish the global existence of strong solution around the equilibrium state 0 c satn 0 with the help of the continuity arguments where c satn is the saturation value of oxygen inside the fluid then we use de giorgi s technique and energy method to show that such a solution will converge to 0 c satn 0 with an explicit convergence rate in the chemotaxis free case our assumptions and results are consistent with the experimental descriptions and the numerical analysis the novelty here consists of deriving some new elliptic estimates and stokes estimates and choosing a suitable weight in de giorgi s technique to deal with the mixed boundary conditions

finite time distributed consensus via binary control protocols this paper investigates the finite time distributed consensus problem for multi agent systems using a binary consensus protocol and the pinning control scheme compared with other consensus algorithms which need the complete state or output information of neighbors the proposed algorithm only requires sign information of the relative state measurements that is the differences between a node s state and that of its neighbors this corresponds to only requiring a single bit quantization error relative to each neighbor this signum protocol is realistic in terms of observed behavior in animal groups where relative motion is determined not by full time signal measurements but by coarse estimates of relative heading differences between neighbors the signum protocol does not require explicit measurement of time signals from neighbors and hence has the potential to significantly reduce the requirements for both computation and sensing analysis of discontinuous dynamical systems is used including the filippov solutions and set valued lie derivative based on the second order information on the evolution of lyapunov functions the conditions that guarantee the finite time consensus for the systems are identified numerical examples are given to illustrate the theoretical results

time global existence and finite time blow up criterion for solutions to the keller segel system coupled with the navier stokes fluid abstract we will deal with the chemotaxis model under the effect of the navier stokes fluid i e the incompressible viscous fluid we shall show the existence of a local mild solution for large initial data and a global mild solution for small initial data in the scale invariant class demonstrating that n 0 l 1 r 2 and u 0 l 2 r 2 our method is based on the perturbation of linearization together with the l p l q estimates of the heat semigroup as a by product of our method we shall prove the smoothing effect and uniqueness of our mild solution in addition we shall show a blow up criterion which almost covers the well known threshold number 8 of the size n 0 l 1 r 2 under the rest state of the fluid motion furthermore the blow up rate will be also discussed

finite time consensus on strongly convex balls of riemannian manifolds with switching directed communication topologies abstract it is known that a consensus problem on any connected complete riemannian manifold can be transformed into the one on its strongly convex balls via the compression decompression along geodesics from the viewpoint of interior metrics this paper mainly provides a consensus protocol for strongly convex geodesic balls in which the communication can be switching and directed with the aid of nonsmooth analysis tools on riemannian manifolds our analysis shows that all dynamical points involved can achieve consensus in finite time meanwhile the corresponding global algorithm is given with its application to the consensus problem of rotation attitudes as well as a case simulation to demonstrate and verify our proposed techniques

consensus seeking in multiagent systems under dynamically changing interaction topologies this note considers the problem of information consensus among multiple agents in the presence of limited and unreliable information exchange with dynamically changing interaction topologies both discrete and continuous update schemes are proposed for information consensus this note shows that information consensus under dynamically changing interaction topologies can be achieved asymptotically if the union of the directed interaction graphs have a spanning tree frequently enough as the system evolves

existence and uniqueness of mild solutions to the incompressible nematic liquid crystal flow abstract in this paper we consider the incompressible nematic liquid crystal flow in the whole space and obtain the existence of global mild solutions with small initial data in the scaling invariant space the main tool we have used is the implicit function theorem furthermore we establish the asymptotic stability of solutions when the time goes to infinity and in view of our construction of solutions in the weak l p spaces we finally derive the existence of self similar solutions provided the initial data are small homogeneous functions

finite time convergent gradient flows with applications to network consensus this paper introduces the normalized and signed gradient dynamical systems associated with a differentiable function extending recent results on nonsmooth stability analysis we characterize their asymptotic convergence properties and identify conditions that guarantee finite time convergence we discuss the application of the results to consensus problems in multi agent systems and show how the proposed nonsmooth gradient flows achieve consensus in finite time

consensus on compact riemannian manifolds in view of a fact that compact manifolds have the important application in practice this paper provides a local consensus protocol for connected compact riemannian manifolds where communication network can be directed and dynamically switching meanwhile with the help of the compression decompression functions we extend the local protocol and propose a global consensus algorithm for such manifolds furthermore to demonstrate their effectiveness and efficiency the global algorithm is applied to the consensus problem of rotation attitudes together with a case simulation

an invariance principle for nonlinear switched systems abstract in this paper we address the problem of extending lasalle invariance principle to switched system we prove an extension of the invariance principle relative to dwell time switched solutions and a second one relative to constrained switched systems

consensus analysis and design for high order linear swarm systems with time varying delays abstract consensus analysis and design problems for high order linear time invariant swarm systems with time varying delays are dealt with first a consensus subspace and a complement consensus subspace are introduced by the state projection onto the two subspaces consensus problems are converted into simultaneous stabilization problems of multiple time delayed subsystems with low dimensions and a method to analyze and design the consensus function is given then sufficient conditions for consensus and consensualization are presented which include only four linear matrix inequality constraints finally theoretical results are applied to deal with cooperative control problems of multi agent supporting systems

non linear protocols for optimal distributed consensus in networks of dynamic agents we consider stationary consensus protocols for networks of dynamic agents with fixed topologies at each time instant each agent knows only its and its neighbors state but must reach consensus on a group decision value that is function of all the agents initial state we show that the agents can reach consensus if the value of such a function is time invariant when computed over the agents state trajectories we use this basic result to introduce a non linear protocol design rule allowing consensus on a quite general set of values such a set includes e g any generalized mean of order p of the agents initial states as a second contribution we show that our protocol design is the solution of individual optimizations performed by the agents this notion suggests a game theoretic interpretation of consensus problems as mechanism design problems under this perspective a supervisor entails the agents to reach a consensus by imposing individual objectives we prove that such objectives can be chosen so that rational agents have a unique optimal protocol and asymptotically reach consensus on a desired group decision value we use a lyapunov approach to prove that the asymptotical consensus can be reached when the communication links between nearby agents define a time invariant undirected network finally we perform a simulation study concerning the vertical alignment maneuver of a team of unmanned air vehicles

global existence and stabilization in a degenerate chemotaxis stokes system with mildly strong diffusion enhancement abstract a class of chemotaxis stokes systems generalizing the prototype n t u n n m 1 n n c c t u c c n c u t p u n u 0 is considered in bounded convex three dimensional domains where w 2 is given the paper develops an analytical approach which consists in a combination of energy based arguments and maximal sobolev regularity theory and which allows for the construction of global bounded weak solutions to an associated initial boundary value problem under the assumption that 0 1 m 9 8 moreover the obtained solutions are shown to approach the spatially homogeneous steady state 1 n 0 0 0 in the large time limit this extends previous results which either relied on different and apparently less significant energy type structures or on completely alternative approaches and thereby exclusively achieved comparable results under hypotheses stronger than 0 1

boundedness in a 2d chemotaxis stokes system with general sensitivity and nonlinear diffusion abstract this paper deals with the following chemotaxis stokes system n t u n n m n s x n c c x t 0 c t u c c n f c x t 0 u t u p n x t 0 u 0 x t 0 in a bounded domain r 2 with smooth boundary w 1 f and s are given sufficiently smooth functions with values in 0 and r 2 2 respectively here s satisfies s x n c s 0 c n with 0 and some nondecreasing nonnegative function s 0 it is showed that when m 1 and 0 the corresponding system possesses a global bounded weak solution for any sufficiently regular initial data n 0 c 0 u 0 satisfying n 0 0 and c 0 0

consensus optimization on manifolds the present paper considers distributed consensus algorithms that involve n agents evolving on a connected compact homogeneous manifold the agents track no external reference and communicate their relative state according to a communication graph the consensus problem is formulated in terms of the extrema of a cost function this leads to efficient gradient algorithms to synchronize i e maximizing the consensus or balance i e minimizing the consensus the agents a convenient adaptation of the gradient algorithms is used when the communication graph is directed and time varying the cost function is linked to a specific centroid definition on manifolds introduced here as the induced arithmetic mean that is easily computable in closed form and may be of independent interest for a number of manifolds the special orthogonal group so n and the grassmann manifold text it grass p n are treated as original examples a link is also drawn with the many existing results on the circle

global existence in critical besov spaces for the coupled chemotaxis fluid equations abstract in this paper we are concerned with a system coupling the parabolic parabolic keller segel system to the viscous incompressible navier stokes equations in spatial dimensions three and prove the global existence of solutions with small initial data in critical besov spaces with minimal regularity order by using the elementary paradifferential calculus and a special type of iteration scheme

eventual smoothness of generalized solutions to a singular chemotaxis stokes system in 2d abstract we study the chemotaxis fluid system n t u n n n c c x t 0 c t u c c n c x t 0 u t p u n x t 0 u 0 x t 0 under homogeneous neumann boundary conditions for n and c and homogeneous dirichlet boundary conditions for u where r 2 is a bounded domain with smooth boundary and c 2 from recent results it is known that for suitable regular initial data the corresponding initial boundary value problem possesses a global generalized solution we will show that for small initial mass n 0 these generalized solutions will eventually become classical solutions of the system and obey certain asymptotic properties moreover from the analysis of certain energy type inequalities arising during the investigation of the eventual regularity we will also derive a result on global existence of classical solutions under assumption of certain smallness conditions on the size of n 0 in l 1 and in l log l u 0 in l 4 and of c 0 in l 2

stability of multiagent systems with time dependent communication links we study a simple but compelling model of network of agents interacting via time dependent communication links the model finds application in a variety of fields including synchronization swarming and distributed decision making in the model each agent updates his current state based upon the current information received from neighboring agents necessary and or sufficient conditions for the convergence of the individual agents states to a common value are presented thereby extending recent results reported in the literature the stability analysis is based upon a blend of graph theoretic and system theoretic tools with the notion of convexity playing a central role the analysis is integrated within a formal framework of set valued lyapunov theory which may be of independent interest among others it is observed that more communication does not necessarily lead to faster convergence and may eventually even lead to a loss of convergence even for the simple models discussed in the present paper