balancing for a class of non linear singularly perturbed systems in this work a balancing method is investigated for a class of non linear singularly perturbed systems the main result presented here shows that the well known two stages strategy used with singular perturbations in control theory can be extended to compute a balancing form of non linear singularly perturbed systems so an approximate balancing form is derived from the balancing forms of the slow and fast subsystems both computed separately this two stage method avoids the difficult task of solving high dimensional and ill conditioned hamilton jacobi equations due to the presence of the small singular perturbation parameter

stabilization and regulation of nonlinear singularly perturbed systems composite control for a general class of nonlinear singularly perturbed systems a two time scale analysis and design procedure for stabilization and regulation is presented it is shown that under a set of conditions the composite control proposed by chow and kokotovic 5 asymptotically stabilizes the desired equilibrium and produces a finite cost j uc which tends to the cost of the slow regulator as the perturbation parameter e tends to zero thus the well posedness of the full regulator problem is established furthermore under different stability requirements on the fast subsystem explicit upper and lower bounds on j uc are obtained finally for each result in this paper an upper bound on the perturbation parameter e is provided under which the result is valid

stochastic analysis of transport in tubes with rough walls flow and transport in tubes with rough surfaces play an important role in a variety of applications often the topology of such surfaces cannot be accurately described in all of its relevant details due to either insufficient data or measurement errors or both in such cases this topological uncertainty can be efficiently handled by treating rough boundaries as random fields so that an underlying physical phenomenon is described by deterministic or stochastic differential equations in random domains to deal with this class of problems we use a computational framework which is based on stochastic mappings to transform the original deterministic stochastic problem in a random domain into a stochastic problem in a deterministic domain the latter problem has been studied more extensively and existing analytical numerical techniques can be readily applied in this paper we employ both a generalized polynomial chaos and monte carlo simulations to solve the transformed stochastic problem we use our approach to describe transport of a passive scalar in stokes flow and to quantify the corresponding predictive uncertainty

new results on composite control of singularly perturbed uncertain linear systems abstract we consider the problem of stabilizing uncertain singularly perturbed linear time varying systems whose fast dynamics can be unstable we propose a class of nonlinear composite controllers which assure global uniform ultimate boundedness of the trajectories of the closed loop system provided the singular perturbation parameter is sufficiently small these controllers consist of a fast controller which stabilizes the fast dynamics and a slow controller which yields the desired stability properties for the slow dynamics we consider the structure of the fast controller to be simpler than structures previously proposed in the literature to obtain these controllers we first develop some new results for singularly perturbed systems under output feedback in particular it is shown that the matching assumption which deals with the manner in which the uncertainties enter the system and is made on the reduced order system is invariant under linear feedback of the fast variable

on the vanishing viscosity limit for the 3d navier stokes equations with a slip boundary condition where and below and denote the div and curl operators respectively n is the outward normal and is the unit tangential vector of the investigation of vanishing viscosity limit of solutions of the navier stokes equations both in the two and three spacial dimensional cases is a classical issue there are two related questions arising from here one is how to describe the inviscid limiting behavior of the navier stokes equation and the other is that does the euler equation can be approximated by the navier stokes equations in the case that the solution to the this research is supported in part by zheng ge ru foundation and hong kong rgc earmarked research grants cuhk 4028 04p cuhk 4040 02p and cuhk 4279 00p

spin and wedge representations of infinite dimensional lie algebras and groups abstract we suggest a purely algebraic construction of the spin representation of an infinite dimensional orthogonal lie algebra sections 1 and 2 and a corresponding group section 4 from this we deduce a construction of all level one highest weight representations of orthogonal affine lie algebras in terms of creation and annihilation operators on an infinite dimensional grassmann algebra section 3 we also give a similar construction of the level one representations of the general linear affine lie algebra in an infinite dimensional wedge space along these lines we construct the corresponding representations of the universal central extension of the group sln k t t 1 in spaces of sections of line bundles over infinite dimensional homogeneous spaces section 5

geometric regularity criteria for incompressible navier stokes equations with navier boundary conditions abstract we study the regularity criteria for weak solutions to the 3d incompressible navier stokes equations in terms of the direction of vorticity taking into account the boundary conditions a boundary regularity theorem is proved on regular curvilinear domains with a family of oblique derivative boundary conditions provided that the directions of vorticity are coherently aligned up to the boundary as an application we establish the boundary regularity for weak solutions to navier stokes equations in round balls half spaces and right circular cylindrical ducts subject to the classical navier and kinematic boundary conditions

on the asymptotic limit of the navier stokes system on domains with rough boundaries abstract we study the asymptotic behavior of solutions to the incompressible navier stokes system considered on a sequence of spatial domains whose boundaries exhibit fast oscillations with amplitude and characteristic wave length proportional to a small parameter imposing the complete slip boundary conditions we show that in the asymptotic limit the fluid sticks completely to the boundary provided the oscillations are non degenerate meaning not oriented in a single direction

model order reduction of random parameter dependent linear systems this paper proposes a new method to perform model reduction of linear time invariant lti systems where parameters are random variables governed by probabilistic laws it combines the well known truncation balanced realization tbr technique together with the generalized polynomial chaos gpc formalism a powerful tool for uncertainty propagation gpc formalism is used to represent and compute a random parameter dependent balancing transformation rpd bt which puts the random lti system in a balanced form almost surely within the probabilistic range of the uncertain parameters model reduction is then performed by truncating almost surely weakly controllable and observable states yielding a random parameter dependent truncated balanced realization rpd tbr the truncation error s moments are shown to be bounded by hankel singular values moments which are also estimated using gpc formalism as an illustrative example the proposed method is applied to a simple mechanical model of a two degrees of freedom mass spring system with uncertain stiffness and damping

on the roughness induced effective boundary conditions for an incompressible viscous flow abstract we consider the laminar viscous channel flow with the lateral surface of the channel containing surface irregularities it is supposed that a uniform pressure gradient is maintained in the longitudinal direction of the channel after studying the corresponding boundary layers we obtain rigorously the navier friction condition it is valid when the size and amplitude of the imperfections tend to zero furthermore the coefficient in the law is determined through an auxiliary boundary layer type problem and the tangential drag force and the effective mass flow are determined up to order o e3 2 the value of the effective coefficient is shown to be independent with respect to the position of the mean surface in the range of o e

the navier slip thin film equation for 3d fluid films existence and uniqueness abstract we consider the thin film equation t h h 2 h 0 in physical space dimensions i e one dimension in time t and two lateral dimensions with h denoting the height of the film in the third spatial dimension which corresponds to the lubrication approximation of the navier stokes equations of a three dimensional viscous thin fluid film with navier slip at the substrate this equation can have a free boundary the contact line moving with finite speed at which we assume a zero contact angle condition complete wetting regime previous results have focused on the 1 1 dimensional version where it has been found that solutions are not smooth as a function of the distance to the free boundary in particular a well posedness and regularity theory is more intricate than for the second order counterpart the porous medium equation or the thin film equation with linear mobility corresponding to darcy dynamics in the hele shaw cell here we prove existence and uniqueness of classical solutions that are perturbations of an asymptotically stable traveling wave profile this leads to control on the free boundary and in particular its velocity

mhd flow in a rectangular duct with a perturbed boundary abstract the unsteady magnetohydrodynamic mhd flow of a viscous incompressible and electrically conducting fluid in a rectangular duct with a perturbed boundary is investigated a small boundary perturbation e is applied on the upper wall of the duct which is encountered in the visualization of the blood flow in constricted arteries the mhd equations which are coupled in the velocity and the induced magnetic field are solved with no slip velocity conditions and by taking the side walls as insulated and the hartmann walls as perfectly conducting both the domain boundary element method dbem and the dual reciprocity boundary element method drbem are used in spatial discretization with a backward finite difference scheme for the time integration these mhd equations are decoupled first into two transient convection diffusion equations and then into two modified helmholtz equations by using suitable transformations then the dbem or drbem is used to transform these equations into equivalent integral equations by employing the fundamental solution of either steady state convection diffusion or modified helmholtz equations the dbem and drbem results are presented and compared by equi velocity and current lines at steady state for several values of hartmann number and the boundary perturbation parameter

feedback control of two time scale nonlinear systems this article concerns a class of two time scale single input single output nonlinear systems for such systems combination of singular perturbation and geometric methods is employed to synthesize well conditioned static state feedback laws that induce a well characterized input output behaviour and guarantee stability of the closed loop system the developed control laws are applied to two nonlinear chemical processes with time scale multiplicity and their performance is evaluated through simulations

gevrey regularity for navier stokes equations under lions boundary conditions abstract the navier stokes system is considered in a compact riemannian manifold gevrey class regularity is proven under lions boundary conditions in 2d for the rectangle cylinder and hemisphere and in 3d for the rectangle the cases of the 2d sphere and 2d and 3d torus are also revisited

average of the navier s law on the rapidly oscillating boundary we study the flow of newtonian fluid in a domain with periodically wrinkled boundary with slip navier s boundary condition the goal of this paper is to replace a microscopic boundary condition posed on the rough boundary by some macroscopic boundary condition posed on the middle surface of the oscillating boundary depending on the shape of wrinkles and the friction coefficient we get four different effective models

flows of incompressible viscous liquids with anisotropic wall slip abstract this paper deals with a boundary value problem for the stokes equations with a general direction dependent navier type slip boundary condition this problem models the steady laminar flow of an incompressible linearly viscous liquid in a bounded domain with an impermeable rough boundary with variable and anisotropic roughness it is proved that the problem has a unique weak solution

droplet spreading intermediate scaling law by pde methods we consider the spreading of a thin droplet of viscous liquid on a plane surface driven by capillarity the standard lubrication approximation leads to an evolution equation for the film height h that is ill posed when the spreading is limited by the no slip boundary condition at the liquid solid interface due to a singularity at the moving contact line the most common relaxation of the no slip boundary condition removes this singularity but introduces a new physical length scale the slippage length b it is believed that this microscopic length scale only enters logarithmically in the effective that is macroscopic spreading behavior in this paper we rigorously show that the naively expected spreading rate is indeed only altered by a logarithmic term involving b more precisely we prove a scaling law for the diameter of the apparent that is macroscopic support of the droplet in time this is an intermediate scaling law it takes an initial layer to forget the initial droplet shape whereas after a long time the droplet is so thin that its spreading is governed by the physics on the scale b our proof works by deriving suitable estimates for physically relevant integral quantities the free energy the length of the apparent support and their respective rates of change as opposed to matched asymptotic methods this pde approach closely mimics a simple heuristic argument based on the gradient flow structure 2002 john wiley sons inc

principal component analysis in linear systems controllability observability and model reduction kalman s minimal realization theory involves geometric objects controllable unobservable subspaces which are subject to structural instability specifically arbitrarily small perturbations in a model may cause a change in the dimensions of the associated subspaces this situation is manifested in computational difficulties which arise in attempts to apply textbook algorithms for computing a minimal realization structural instability associated with geometric theories is not unique to control it arises in the theory of linear equations as well in this setting the computational problems have been studied for decades and excellent tools have been developed for coping with the situation one of the main goals of this paper is to call attention to principal component analysis hotelling 1933 and an algorithm golub and reinsch 1970 for computing the singular value decompositon of a matrix together they form a powerful tool for coping with structural instability in dynamic systems as developed in this paper principal component analysis is a technique for analyzing signals singular value decomposition provides the computational machinery for this reason kalman s minimal realization theory is recast in terms of responses to injected signals application of the signal analysis to controllability and observability leads to a coordinate system in which the internally balanced model has special properties for asymptotically stable systems this yields working approximations of x c x bar o the controllable and unobservable subspaces it is proposed that a natural first step in model reduction is to apply the mechanics of minimal realization using these working subspaces

a combined finite element method for elliptic problems posted in domains with rough boundaries abstract a combined finite element method is presented in this paper to solve the elliptic problems posted in domains with rough boundaries solving these problems numerically is difficult because resolving the boundaries usually requires very fine meshes while good quality meshes often over refine unnecessarily the interior of the domain the basic idea of the proposed method is to use a fine mesh with size h in the vicinity of oscillating boundaries and a coarse mesh with size h h for other portions of the domain to reduce some unnecessary computational effort the transmission conditions across the fine coarse mesh interface are treated by the penalty technique the key point of the method lies in the new scheme employing a weighted average in the definition of the bilinear form which avoids the affection of the ratio h h in the error estimate we prove a quasi optimal convergence in terms of elements since there is no whole h 2 regularity in the domain with rough boundaries numerical results are provided for elliptic equations in domains with non oscillating or oscillating boundaries to illustrate the theoretical results

vanishing viscosity limit for the 3d magnetohydrodynamic system with a slip boundary condition abstract this work investigates the solvability regularity and vanishing viscosity limit of the 3d viscous magnetohydrodynamic system in a class of bounded domains with a slip boundary condition

semi group theory for the stokes operator with navier type boundary conditions on l p spaces in this article we consider the stokes problem with navier type boundary conditions on a domain omega not necessarily simply connected since under these conditions the stokes problem has a non trivial kernel we also study the solutions lying in the orthogonal of that kernel we prove the analyticity of several semigroups generated by the stokes operator considered in different functional spaces we obtain strong weak and very weak solutions for the time dependent stokes problem with the navier type boundary condition under different hypotheses on the initial data u0 and external force f then we study the fractional and pure imaginary powers of several operators related with our stokes operators using the fractional powers we prove maximal regularity results for the homogeneous stokes problem on the other hand using the boundedness of the pure imaginary powers we deduce maximal l p l q regularity for the inhomogeneous stokes problem

two constructions of affine lie algebra representations and boson fermion correspondence in quantum field theory we establish an isomorphism between the vertex and spinor representations of affine lie algebras for types dl 1 and dl 1 2 we also study decomposition of spinor representations using the infinite family of casimir operators and prove that they are either irreducible or have two irreducible components we show that the vertex and spinor constructions of the representations can be reformulated in the language of two dimensional quantum field theory in this physical context the two constructions yield the generalized sine gordon and thirring models respectively already in renormalized form the isomorphism of representations implies an equivalence of these two models which is known in quantum field theory as the boson fermion correspondence

representations of the sl 2 c kac moody current algebra in the fock space a representation of the sl 2 c current algebra in terms of hermitian currents constructed from free fields is obtained the representation is not of the highest weight type the restriction k 4 on the kac moody central charge k is obtained if k 4 then the sugawara construction defines the energy momentum tensor equal to the energy momentum tensor of the free field theory

boundary behavior of viscous fluids influence of wall roughness and friction driven boundary conditions we consider a family of solutions to the evolutionary navier stokes system supplemented with the complete slip boundary conditions on domains with rough boundaries we give a complete description of the asymptotic limit by means of convergence arguments and identify a general class of boundary conditions

numerical approximation of laminar flows over rough walls with sharp asperities abstract we consider a viscous incompressible fluid filling an infinite horizontal domain bounded at the bottom by a plane wall and at the top by a rough wall the latter is assumed to consist of a plane wall covered with periodically distributed asperities whose size depends on a small parameter e 0 the assumption of sharp asperities is made that is the height of the asperities does not vanish as e 0 the rough wall is at rest and the plane wall is moving at a constant horizontal velocity we assume that the flow is governed by the stationary stokes equations we give an asymptotic approximation of the stokes flow under the rugose region by a couette flow depending on the size e of the asperities we then build a numerical approximation of the couette flow based on a partial domain decomposition method

viscous boundary layers for the navier stokes equations with the navier slip conditions we tackle the issue of the inviscid limit of the incompressible navier stokes equations when the navier slip with friction conditions are prescribed on impermeable boundaries we justify an asymptotic expansion which involves a weak amplitude boundary layer with the same thickness as in prandtl s theory and a linear behavior this analysis holds for general regular domains in both dimensions two and three

effective boundary condition for stokes flow over a very rough surface abstract the main purpose of this paper is to derive a wall law for a flow over a very rough surface we consider a viscous incompressible fluid filling a 3 dimensional horizontal domain bounded at the bottom by a smooth wall and at the top by a very rough wall the latter consists in a plane wall covered with periodically distributed asperities which size depends on a small parameter e 0 and with a fixed height we assume that the flow is governed by the stationary stokes equations using asymptotic expansions and boundary layer correctors we construct and analyze an asymptotic approximation of order o e 3 2 0 being arbitrary small in the h 1 norm for the velocity and in the l 2 norm for the pressure we derive an effective boundary condition of navier type then expressing the boundary layer terms in terms of the homogenized solution and the solution of a cell problem we obtain an effective approximation in the whole domain of the flow

a shape hessian based boundary roughness analysis of navier stokes flow the influence of boundary roughness characteristics on the rate of dissipation in a viscous fluid is analyzed using shape calculus from the theory of optimal control of systems governed by partial differential equations to study the mapping mathscr d from surface roughness topography to the dissipation rate of a navier stokes flow expressions for the shape gradient and hessian are determined using the velocity method in the case of couette and poiseuille flows a flat boundary is a local minimum of the dissipation rate functional thus for small roughness heights the behavior of mathscr d is governed by the flat wall shape hessian operator whose eigenfunctions are shown to be the fourier modes for stokes flow the shape hessian is determined analytically and its eigenvalues are shown to grow linearly with the wavenumber of the shape perturbation for navier stokes flow the shape hessian is computed numerically and the ratio of its eigenvalues to those of a stokes flow depend only on the re

on the vanishing viscosity limit of 3d navier stokes equations under slip boundary conditions in general domains we consider the vanishing viscosity limit for the navier stokes equations with certain slip without friction boundary conditions in a bounded domain with non flat boundary in particular we are able to show convergence in strong norms for a solution starting with initial data belonging to the special subclass of data with vanishing vorticity on the boundary the proof is obtained by smoothing the initial data and by a perturbation argument with quite precise estimates for the equations of the vorticity and for that of the curl of the vorticity

robust semi global output tracking for nonlinear singularly perturbed systems in this work a robust controller design methodology for a broad class of singularly perturbed nonlinear systems with time varying uncertainties is developed when the fast subsystem is stabilizable and the slow subsystem is input output linearizable with input to state stable iss inverse dynamics the developed state feedback controller guarantees boundedness of the trajectories of the closed loop system and robust output tracking with arbitrary degree of asymptotic attenuation of the effect of uncertainty on the output for initial conditions and uncertainties in an arbitrarily large compact set so long as the singular perturbation parameter is sufficiently small the controller is a continuous function of the state of the system and its construction requires the knowledge of bounding functions on the size of uncertainty the developed method is applied to a non isothermal continuous stirred tank reactor with fast jacket dynamics

effective boundary conditions for laminar flows over periodic rough boundaries effective boundary conditions or wall laws are proposed for a laminar flow over a rough wall with periodic roughness elements these effective conditions are posed on a regularized boundary which allows the details of the wall to be avoided and dramatically reduces the computational cost the effective conditions stem from an asymptotic expansion of the solution which is presented here both first and second order conditions are discussed and tested numerically on bidimensional cases

vanishing viscosity limit for incompressible navier stokes equations with navier boundary conditions for small slip length in this paper we will analyze the vanishing viscosity limit of the incompressible navier stokes equations with the navier slip boundary conditions in a bounded domain of r2 when the slip length is smaller than or equal to the order of viscosity by using an energy method and developing kato s approach given in the work of kato math sci res inst publ 2 85 98 1984 we obtain several conditions to guarantee that the solution of the navier stokes equations with the navier slip boundary conditions goes to the solution of the associated problem of the euler equations in the energy space l2 uniformly in time as the viscosity goes to zero

artificial conditions for the linear elasticity equations in this paper we consider the equations of linear elasticity in an exterior domain we exhibit artificial boundary conditions on a circle which lead to a non coercive second order boundary value problem in the particular case of an axisymmetric geometry explicit computations can be performed in fourier series proving the well posedness except for a countable set of parameters a perturbation argument allows to consider near circular domains we complete the analysis by some numerical simulations

model reduction via balanced state space representations a model reduction procedure based on balanced state space representations is studied in this paper the reduced order model is examined from the point of view of stability controllability and observability both continuous time and discrete time systems are considered

upper bounds on waiting times for the thin film equation the case of weak slippage we derive upper bounds on the waiting time of solutions to the thin film equation in the regime of weak slippage n in 2 frac 32 11 in particular we give sufficient conditions on the initial data for instantaneous forward motion of the free boundary for n in 2 frac 32 11 our estimates are sharp for n 2 they are sharp up to a logarithmic correction term note that the case n 2 corresponds with a grain of salt to the assumption of the navier slip condition at the fluid solid interface we also obtain results in the regime of strong slippage n in 1 2 however in this regime we expect them not to be optimal our method is based on weighted backward entropy estimates hardy s inequality and singular weight functions we deduce a differential inequality which would enforce blowup of the weighted entropy if the contact line were to remain stationary for too long

relevance of the slip condition for fluid flows near an irregular boundary we consider the navier stokes equation in a domain with a rough boundary the roughness is modeled by a small amplitude and small wavelength oscillation with typical scale varepsilon ll 1 for periodic oscillation it is well known that the best homogenized that is regular in varepsilon boundary condition is of navier type such result still holds for random stationary irregularities as shown recently by the first author 5 15 we study here arbitrary irregularity patterns

roughness induced effects on the quasi geostrophic model we study in this paper the effect of small scale irregularities on the quasi geostrophic model this study is motivated by some problems related to oceanography as the gulf stream separation or the impact of the topography on the global circulation we first consider the role of coastal roughness in the phenomenon of western intensification of boundary currents we show that the roughness is responsible for a nonlinear dynamics of the boundary layers governed by a quasilinear elliptic equation we thus extend substantially the classical derivation of munk layers 15 and the results of convergence obtained in 10 we then discuss the effect of a rough topography by generalizing and justifying some formal computations of 17 in particular we derive rigorously a simplified model of oceanic circulation with a nonlinear and nonlocal dissipative term due to the roughness

effective boundary condition at a rough surface starting from a slip condition abstract we consider the homogenization of the navier stokes equation set in a channel with a rough boundary of small amplitude and wavelength it was shown recently that for any non degenerate roughness pattern and for any reasonable condition imposed at the rough boundary the homogenized boundary condition in the limit e 0 is always no slip we give in this paper error estimates for this homogenized no slip condition and provide a more accurate effective boundary condition of navier type our result extends those obtained in basson and gerard varet 2008 6 and gerard varet and masmoudi 2010 13 in which the special case of a dirichlet condition at the rough boundary was examined

representation of the affine superalgebras a 4 0 2l a 2 0 2l 1 and their subalgebras a2l 2 a2l 1 2 by vertex operators abstract the structure theory of standard modules of affine lie algebras given by j lepowsky and r l wilson in lw is stated for representations of affine superalgebras as an application the standard modules of level one for the superalgebras a 4 0 2l a 2 0 2l 1 and their affine subalgebras a2l 2 a2l 1 2 are constructed explicitly these modules are realized as the tensor product of symmetric and exterior algebras with an irreducible representation of a certain finite 2 group the affine superalgebra acts on this space by tensor products of vertex operators operators of clifford type and elements of the 2 group as a corollary the spin representations of the lie algebras bl and dl are obtained from the 2 group representation

navier stokes equations in 3d thin domains with navier friction boundary condition abstract in this article we study the 3d navier stokes equations with navier friction boundary condition in thin domains we prove the global existence of strong solutions to the 3d navier stokes equations when the initial data and external forces are in large sets as the thickness of the domain is small we generalize the techniques developed to study the 3d navier stokes equations in thin domains see g raugel g sell navier stokes equations on thin 3d domains i global attractors and global regularity of solutions j amer math soc 6 1993 503 568 g raugel g sell navier stokes equations on thin 3d domains ii global regularity of spatially periodic conditions in nonlinear partial differential equations and their application college de france seminar vol xi longman harlow 1994 pp 205 247 r temam m ziane navier stokes equations in three dimensional thin domains with various boundary conditions adv differential equations 1 1996 499 546 r temam m ziane navier stokes equations in thin spherical shells in optimization methods in partial differential equations in contemp math vol 209 amer math soc providence ri 1996 pp 281 314 to the navier friction boundary condition by introducing a new average operator m e in the thin direction according to the spectral decomposition of the stokes operator a e our analysis hinges on the refined investigation of the eigenvalue problem corresponding to the stokes operator a e with navier friction boundary condition

existence of a weak solution to a fluid elastic structure interaction problem with the navier slip boundary condition abstract we study a nonlinear moving boundary fluid structure interaction fsi problem between an incompressible viscous newtonian fluid modeled by the 2d navier stokes equations and an elastic structure modeled by the shell or plate equations the fluid and structure are coupled via the navier slip boundary condition and balance of contact forces at the fluid structure interface the slip boundary condition might be more realistic than the classical no slip boundary condition in situations e g when the structure is rough and in modeling fsi dynamics near or at a contact cardiovascular tissue and cell seeded tissue constructs which consist of grooves in tissue scaffolds that are lined with cells are examples of rough elastic interfaces interacting with an incompressible viscous fluid the problem of heart valve closure is an example of a fsi problem with a contact involving elastic interfaces we prove the existence of a weak solution to this class of problems by designing a constructive proof based on the time discretization via operator splitting this is the first existence result for fluid structure interaction problems involving elastic structures satisfying the navier slip boundary condition

asymptotic behavior of a non newtonian flow in a thin domain with navier law on a rough boundary abstract we consider a non newtonian flow in a thin domain of thickness e the flow is described by the 3d incompressible navier stokes stokes system with a nonlinear viscosity being a power of the shear rate power law of flow index p the bottom of the domain is irregular by the presence of slight roughness of amplitude e and period e satisfying the relation 1 assuming pure slip or partial slip with a friction coefficient e with 0 on the rough boundary we consider the limit when domain thickness tends to zero and we obtain different models depending on the magnitude with respect to 2 p 1 p p 1 p and the magnitude with respect to 1 p 1

a diffuse interface method for the navier stokes darcy equations perfusion profile for a patient specific human liver based on mri scans abstract we present a diffuse interface method for coupling free and porous medium type flows modeled by the navier stokes and darcy equations its essential component is a diffuse geometry model generated from the phase field solution of a separate initial boundary value problem that is based on the allen cahn equation phase field approximations of the interface and its gradient are then employed to transfer all interface terms in the coupled variational flow formulation into volumetric terms this eliminates the need for an explicit interface parametrization between the two flow regimes we illustrate accuracy and convergence for a series of benchmark examples using standard low order stabilized finite element discretizations our diffuse interface method is particularly attractive for coupled flow analysis on imaging data with complex implicit interfaces where procedures for deriving explicit surface parametrizations constitute a significant bottleneck we demonstrate the potential of our method to establish seamless imaging through analysis workflows by computing a perfusion profile for a full scale 3d human liver based on mri scans

weighted hilbert spaces for the stationary exterior stokes problem with navier slip boundary conditions abstract in this paper we analyze the three dimensional exterior stokes problem with the navier slip boundary conditions describing the flow of a viscous and incompressible fluid past an obstacle where it is assumed that the fluid may slip at the boundary because the flow domain is unbounded we set the problem in weighted spaces in order to control the behavior at infinity of the solutions this functional framework also allows to prescribe various behaviors at infinity of the solutions growth or decay existence and uniqueness of solutions are shown in a hilbert setting which gives the tools for a possible numerical analysis of the problem weighted korn s inequalities are the key point in order to study the variational problem

normalized coprime factorizations and balancing for unstable nonlinear systems in this paper we first study the normalized right and left coprime factorizations of a nonlinear system from a state space point of view in order to do so we introduce the notion of inner and co inner nonlinear systems secondly we deal with balancing for unstable nonlinear systems for linear systems there are several ways to approach this problem and we generalize the ideas of balancing the normalized coprime factorization and of lqg balancing to the nonlinear case lqg balancing can be seen as measuring the influence of a state component on a certain future and past energy function we extend this interpretation to the nonlinear case furthermore we use the normalized coprime factorization to give another way of balancing the unstable nonlinear system we give the relation between these two methods of balancing which is similar to the relation in the linear case

effective surface and boundary conditions for heterogeneous surfaces with mixed boundary conditions to deal with multi scale problems involving transport from a heterogeneous and rough surface characterized by a mixed boundary condition an effective surface theory is developed which replaces the original surface by a homogeneous and smooth surface with specific boundary conditions a typical example corresponds to a laminar flow over a soluble salt medium which contains insoluble material to develop the concept of effective surface a multi domain decomposition approach is applied in this framework velocity and concentration at micro scale are estimated with an asymptotic expansion of deviation terms with respect to macro scale velocity and concentration fields closure problems for the deviations are obtained and used to define the effective surface position and the related boundary conditions the evolution of some effective properties and the impact of surface geometry peclet schmidt and damkohler numbers are investigated finally comparisons are made between the numerical results obtained with the effective models and those from direct numerical simulations with the original rough surface for two kinds of configurations

vanishing viscous limits for the 2d lake equations with navier boundary conditions abstract the vanishing viscosity limit is considered for the viscous lake equations with navier friction boundary conditions we prove that the inviscid limit satisfies the inviscid lake equations and the results include flows generated by l p initial vorticity with 1 p

wall laws for fluid flows at a boundary with random roughness the general concern of this paper is the effect of rough boundaries on fluids we consider a stationary flow governed by incompressible navier stokes equations in an infinite domain bounded by two horizontal rough plates the roughness is modeled by a spatially homogeneous random field with characteristic size e a mathematical analysis of the flow for small e is performed the navier s wall law is rigorously deduced from this analysis this substantially extends former results obtained in the case of periodic roughness notably in 16 17 2007 wiley periodicals inc

navier wall law for nonstationary viscous incompressible flows abstract we study the navier wall law for the two dimensional initial boundary value problem of the navier stokes equations in a domain with a rough boundary the navier wall law is verified for the initial data in c 1 class under the natural compatibility condition our proof relies on the boundary layer analysis and the l theory of the navier stokes equations in the half space