dirichlet form approach to infinite dimensional wiener processes with singular interactions we construct infinite dimensional wiener processes with interactions by constructing specific quasi regular dirichlet forms our assumptions are very mild accordingly our results can be applied to singular interactions such as hard core potentials lennard jones type potentials and dyson s model we construct nonequilibrium dynamics

existence and regularity of invariant measures for the three dimensional stochastic primitive equations we establish the continuity of the markovian semigroup associated with strong solutions of the stochastic 3d primitive equations and prove the existence of an invariant measure the proof is based on new moment bounds for strong solutions the invariant measure is supported on strong solutions and is furthermore shown to have higher regularity properties

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

an enhancement of constraint feasibility in bpn based approximate optimization back propagation neural networks bpn have been extensively used as global approximation tools in the context of approximate optimization a traditional bpn is normally trained by minimizing the absolute difference between target outputs and approximate outputs when bpn is used as a meta model for inequality constraint function approximate optimal solutions are sometimes actually infeasible in a case where they are active at the constraint boundary the paper explores the development of the efficient bpn based meta model that enhances the constraint feasibility of approximate optimal solution the bpn based meta model is optimized via exterior penalty method to optimally determine interconnection weights between layers in the network the proposed approach is verified through a simple mathematical function and a ten bar planar truss problem for constrained approximate optimization design of rotor blade is conducted to support the proposed strategies

singularity formation for prandtl s equations abstract we consider prandtl s equations for an impulsively started disk and follow the process of the formation of the singularity in the complex plane using the singularity tracking method we classify van dommelen and shen s singularity as a cubic root singularity we introduce a class of initial data uniformly bounded in h 1 which have a dipole singularity in the complex plane these data lead to a solution blow up whose time can be made arbitrarily short within the class this is numerical evidence of the ill posedness of the prandtl equations in h 1 the presence of a small viscosity in the streamwise direction changes the behavior of the singularities they stabilize at a distance from the real axis which depends on the amount of viscosity we show that the van dommelen and shen singularity and the singularity predicted by e and engquist in w e b engquist blowup of the solutions to the unsteady prandtl s equations comm pure appl math 50 1997 1287 1293 have different complex structures

on the inviscid limit problem of the vorticity equations for viscous incompressible flows in the half plane we consider the navier stokes equations for viscous incompressible flows in the half plane under the no slip boundary condition by using the vorticity formulation we prove the local in time convergence of the navier stokes flows to the euler flows outside a boundary layer and to the prandtl flows in the boundary layer in the inviscid limit when the initial vorticity is located away from the boundary 2014 wiley periodicals inc

sublayer of prandtl boundary layers the aim of this paper is to investigate the stability of prandtl boundary layers in the vanishing viscosity limit nu to 0 in grenier commun pure appl math 53 9 1067 1091 2000 one of the authors proved that there exists no asymptotic expansion involving one of prandtl s boundary layer with thickness of order sqrt nu which describes the inviscid limit of navier stokes equations the instability gives rise to a viscous boundary sublayer whose thickness is of order nu 3 4 in this paper we point out how the stability of the classical prandtl s layer is linked to the stability of this sublayer in particular we prove that the two layers cannot both be nonlinearly stable in l infty that is either the prandtl s layer or the boundary sublayer is nonlinearly unstable in the sup norm

boundary layers associated with incompressible navier stokes equations the noncharacteristic boundary case abstract the goal of this article is to study the boundary layer of wall bounded flows in a channel at small viscosity when the boundaries are uniformly noncharacteristic i e there is injection and or suction everywhere at the boundary following earlier work on the boundary layer for linearized navier stokes equations in the case where the boundaries are characteristic no slip at the boundary and non permeable we consider here the case where the boundary is permeable and thus noncharacteristic the form of the boundary layer and convergence results are derived in two cases linearized equation and full nonlinear equations we prove that there exists a boundary layer at the outlet downwind of the form e uz e where u is the speed of injection suction at the boundary z is the distance to the outlet of the channel and e is the kinematic viscosity we improve an earlier result of s n alekseenko 1994 siberian math j 35 no 2 209 230 where the convergence in l 2 of the solutions of the navier stokes equations to that of the euler equations at vanishing viscosity was established in the two dimensional case we are able to derive the physically relevant uniform in space l norm estimates of the boundary layer the uniform in space estimate is derived by properly developing our previous idea of better control on the tangential derivative and the use of an anisotropic sobolev imbedding to the best of our knowledge this is the first rigorously proved result concerning boundary layers for the full nonlinear navier stokes equations for incompressible fluids

the inviscid limit of navier stokes equations for analytic data on the half space in their classical work sammartino and caflisch commun math phys 192 2 433 461 1998a commun math phys 192 2 463 491 1998b proved the inviscid limit of the incompressible navier stokes equations for well prepared data with analytic regularity in the half space their proof is based on the detailed construction of prandtl s boundary layer asymptotic expansions in this paper we give a direct proof of the inviscid limit for general analytic data without having to construct prandtl s boundary layer correctors our analysis makes use of the boundary vorticity formulation and the abstract cauchy kovalevskaya theorem on analytic boundary layer function spaces that capture unbounded vorticity

dirichlet forms and dirichlet operators for infinite particle systems essential self adjointness we study the dirichlet forms and the associated dirichlet operators for gibbs measures on infinite particle configuration space the dirichlet forms are defined to be gradient type forms by introducing a measurable field of rigged hilbert spaces on the configuration space under mild conditions on the interaction including singular potentials we show that the pre dirichlet operator is symmetric and that the closure of the pre dirichlet form satisfies the markovian property when the interaction is three times differentiable and decreasing sub exponentially we show that the dirichlet operator is essentially self adjoint on a domain consisting of bounded smooth local functions

zero viscosity limit of the navier stokes equations in the analytic setting in this paper we consider the zero viscosity limit of the navier stokes equations in a half space with non slip boundary condition based on the vorticity formulation and the use of conormal derivative we develop an energy method to justify the zero viscosity limit for the analytic data

on the h s theory of hydrostatic euler equations in this paper we study the two dimensional hydrostatic euler equations in a periodic channel we prove the local existence and uniqueness of hs solutions under the local rayleigh condition this extends brenier s nonlinearity 12 3 495 512 1999 existence result by removing an artificial condition and proving uniqueness in addition we prove weak strong uniqueness mathematical justification of the formal derivation and stability of the hydrostatic euler equations these results are based on weighted hs a priori estimates which come from a new type of nonlinear cancellation between velocity and vorticity

a simple global model for the general circulation of the atmosphere in this article we present a new method of rossby asymptotics for the equations of the atmosphere similar to the geostrophic asymptotics we depart from the classical geostrophics see j g charney 5 and our previous article 29 by considering an asymptotics valid for the whole atmosphere not only in midlatitude regions and by taking into account the spherical form of the earth we obtain in this way a very simple global circulation model of the atmosphere for which the equations of motion for wind and temperature are linear evolution equations similar to the linear stokes equations furthermore the solutions are independent of longitude and winds travel exactly to the east or to the west in this mathematically oriented article we do not discuss the physical significance of the model that we derive except for observing that this picture coincides in general terms with the classically averaged data obtained by experimental measurements we also note that different global geostrophic asymptotics called planetary geostrophic asymptotics are considered elsewhere in the literature for example in j pedlosky 33 in a less mathematically rigorous way h lamb 21 observed that the only globally valid geostrophic flow that maintains a slow time scale is zonally symmetric see the comments in n phillips 35 and an explicit derivation in h jeffreys 19 c 1997 john wiley sons inc

blowup of solutions of the unsteady prandtl s equation we prove that for certain class of compactly supported c initial data smooth solutions of the unsteady prandtl s equation blow up in nite time

the inviscid limit for the navier stokes equations with data analytic only near the boundary we address the inviscid limit for the navier stokes equations in a half space with initial datum that is analytic only close to the boundary of the domain and that has sobolev regularity in the complement we prove that for such data the solution of the navier stokes equations converges in the vanishing viscosity limit to the solution of the euler equation on a constant time interval

ergodicity ofl2 semigroups and extremality of gibbs states we extend the classical results of holley stroock on the characterization of extreme gibbs states for the ising model in terms of the irreducibility resp ergodicity of the corresponding glauber dynamics to the case of lattice systems with unbounded linear spin spaces we first develop a general framework to discuss questions of this type using classical dirichlet forms on infinite dimensional state spaces and their associated diffusions we then describe concrete applications to lattice models with polynomial interactions i e the discretep d models of euclidean quantum field theory in addition we prove the equivalence of extremality and shift ergodicity for tempered gibbs states of these models and also discuss this question in the general framework

gevrey stability of prandtl expansions for 2 dimensional navier stokes flows we investigate the stability of boundary layer solutions of the 2 dimensional incompressible navier stokes equations we consider shear flow solutions of prandtl type u t x y ue t y ubl t y 0 0 1 we show that if ubl is monotonic and concave in y y then u is stable over some time interval 0 t t independent of under perturbations with gevrey regularity in x and sobolev regularity in y we improve in this way the classical stability results of sammartino and caflisch in analytic class both in x and y moreover in the case where ubl is steady and strictly concave our gevrey exponent for stability is optimal the proof relies on new and sharp resolvent estimates for the linearized orr sommerfeld operator

equilibrium fluctuations for interacting brownian particles we consider an infinitely extended system of brownian particles interacting by a pair force gradv their initial distribution is stationary and given by the gibbs measure associated with the potentialv with fugacityz we assume thatv is symmetric finite range three times continuously differentiable superstable and positive and that the fugacity is small in the sense that 0 z 0 28 eedq 1 e v q in addition a certain essential self adjointness property is assumed we prove then that the time dependent fluctuations in the density on a spatial scale of order 1 and on a time scale of order 2 converge as 0 to a gaussian field with covariance edqg q e 2 t f q withp the density and the compressibility

local in time existence and uniqueness of solutions to the prandtl equations by energy methods we prove local existence and uniqueness for the two dimensional prandtl system in weighted sobolev spaces under oleinik s monotonicity assumption in particular we do not use the crocco transform or any change of variables our proof is based on a new nonlinear energy estimate for the prandtl system this new energy estimate is based on a cancellation property that is valid under the monotonicity assumption to construct the solution we use a regularization of the system that preserves this nonlinear structure this new nonlinear structure may give some insight into the convergence properties from the navier stokes system to the euler system when the viscosity goes to 0 2015 wiley periodicals inc

genetic search an approach to the nonconvex optimization problem principles of genetics and natural selection are adapted into a search procedure for function optimization such methods are based on a randomized selection from that restricted region of the design space that yields and improvement in the objective function an implementation of the approach to a class of problems in structural optimization with demonstrated nonconvexities or disjointness is discussed in the paper the principal drawback of the method is an increase in function evaluations necessary to locate an optimum possible strategies to overcome this limitation are presented

genetic algorithms in truss topological optimization the present paper describes the use of a stochastic search procedure that is the basis of genetic algorithms in developing near optimal topologies of load bearing truss structures the problem addressed is one wherein the structural geometry is created from a specification of load conditions and available support points in the design space the development of this geometry must satisfy kinematic stability requirements in addition to the usual requirements of structural strength and stiffness the approach is an adaptation of the ground structure method of topology optimization and is implemented in a two level genetic algorithm based search in this process the kinematic stability constraints are imposed at one level followed by the treatment of response constraints at a second level of optimization singular value decomposition is used to assess the kinematic stability constraints at the first level of design and results in the creation of a finite number of increasing weight stable topologies member sizing is then introduced at a second level of design where minimal weight and response constraints on stresses displacements and buckling are simultaneously considered at this level the only admissible topologies are those identified during the first stage and any stable combination thereof the design variable representation scheme allows for both the removal and addition of structural members during optimization

zero viscosity limit for analytic solutions of the navier stokes equation on a half space i existence for euler and prandtl equations this is the first of two papers on the zero viscosity limit for the incompressible navier stokes equations in a half space in this paper we prove short time existence theorems for the euler and prandtl equations with analytic initial data in either two or three spatial dimensions the main technical tool in this analysis is the abstract cauchy kowalewski theorem for the euler equations the projection method is used in the primitive variables to which the cauchy kowalewski theorem is directly applicable for the prandtl equations cauchy kowalewski is applicable once the diffusion operator in the vertical direction is inverted

a well posedness theory for the prandtl equations in three space variables abstract the well posedness of the three space dimensional prandtl equations is studied under some constraint on its flow structure together with the instability result given in 28 it gives an almost necessary and sufficient structural condition for the stability of the three dimensional prandtl equations it reveals that the classical burgers equation plays an important role in determining this type of flow with special structure that avoids the appearance of the secondary flow an unstabilizing factor in the three dimensional prandtl boundary layers and the sufficiency of the monotonicity condition on the tangential velocity field for the existence of solutions to the prandtl boundary layer equations is illustrated in the three dimensional setting moreover it is shown that this structured flow is linearly stable for any smooth three dimensional perturbation

construction of infinite dimensional interacting diffusion processes through dirichlet forms by the theory of quasi regular dirichletforms and the associated special standard processes the existence of symmetric diffusion processes taking values in the space of non negative integer valued radon measures on mbox boldmath r nu and having gibbs invariant measures associated with some given pair potentials is considered the existence of such diffusions can be shown for a wide class of potentials involving some singular ones also as a consequence of an application of stochastic calculus a representation for the diffusion by means of a stochastic differential equation is derived

vanishing viscosity limit for incompressible flow inside a rotating circle abstract in this article we consider circularly symmetric incompressible viscous flow in a disk the boundary condition is no slip with respect to a prescribed time dependent rotation of the boundary about the center of the disk we prove that if the prescribed angular velocity of the boundary has finite total variation then the navier stokes solutions converge strongly in l 2 to the corresponding stationary solution of the euler equations when viscosity vanishes our approach is based on a semigroup treatment of the symmetry reduced scalar equation

a note on prandtl boundary layers this note concerns nonlinear ill posedness of the prandtl equation and an invalidity of asymptotic boundary layer expansions of incompressible fluid flows near a solid boundary our analysis is built upon recent remarkable linear illposedness results established by gerard varet and dormy and an analysis by guo and tice we show that the asymptotic boundary layer expansion is not valid for nonmonotonic shear layer flows in sobolev spaces we also introduce a notion of weak well posedness and prove that the nonlinear prandtl equation is not well posed in this sense near nonstationary and nonmonotonic shear flows on the other hand we are able to verify that oleinik s monotonic solutions are well posed 2011 wiley periodicals inc

local existence and uniqueness for the hydrostatic euler equations on a bounded domain abstract we address the question of well posedness in spaces of analytic functions for the cauchy problem for the hydrostatic incompressible euler equations inviscid primitive equations on domains with boundary by a suitable extension of the cauchy kowalewski theorem we construct a locally in time unique real analytic solution and give an explicit rate of decay of the radius of real analyticity

on the vanishing viscosity limit in a disk we say that a solution of the navier stokes equations converges in the vanishing viscosity limit to a solution of the euler equations if their velocities converge in the energy l2 norm uniformly in time as the viscosity vanishes we show that a necessary and sufficient condition for the vanishing viscosity limit to hold in a disk is that the space time energy density of the solution to the navier stokes equations in a boundary layer of width proportional to vanish with and that one need only consider spatial variations whose frequencies in the radial or tangential direction lie in a band centered around 1

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

almost global existence for the prandtl boundary layer equations we consider the prandtl boundary layer equations on the half plane with initial datum that lies in a weighted h1 space with respect to the normal variable and is real analytic with respect to the tangential variable the boundary trace of the horizontal euler flow is taken to be a constant we prove that if the prandtl datum lies within varepsilon of a stable profile then the unique solution of the cauchy problem can be extended at least up to time t varepsilon geqq rm exp varepsilon 1 rm log varepsilon 1

dirichlet forms and diffusion processes for fermion random point fields abstract we construct the dirichlet forms and the associated diffusion processes on the configuration space of particles moving on the euclidean space r d for which certain fermion random point fields are invariant

the euler limit of the navier stokes equations and rotating fluids with boundary in this paper we study the convergence of weak solutions of the navier stokes equations in some particular domains with different horizontal and vertical viscosities when they go to zero with different speeds the difficulty here comes from the dirichlet boundary conditions precisely we show that if the ratio of the vertical viscosity to the horizontal viscosity also goes to zero then the solutions converge to the solution of the euler system we study the same limit for rotating fluids with rossby number also going to zero

nonequilibrium dynamics of infinite particle systems with infinite range interactions we discuss the existence and uniqueness of nonequilibrium dynamics of infinitely many particles interacting via superstable pair interactions in one and two dimensions the interaction is allowed to be of infinite range and singular at the origin under suitable regularity conditions on the interaction potential we show that if the potential decreases polynomially as the distance between interacting two particles increases then the tempered solution to the system of hamiltonian equations exists moreover if the potential satisfies further that either it has a subexponential decreasing rate or it is everywhere two times continuously differentiable then we show that the tempered solution is unique the results extend those of dobrushin and fritz obtained for finite range interactions

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

zero viscosity limit for analytic solutions of the navier stokes equation on a half space ii construction of the navier stokes solution this is the second of two papers on the zero viscosity limit for the incompressible navier stokes equations in a half space in either 2d or 3d under the assumption of analytic initial data we construct solutions of navier stokes for a short time which is independent of the viscosity the navier stokes solution is constructed through a composite asymptotic expansion involving the solutions of the euler and prandtl equations which were constructed in the first paper plus an error term this shows that the navier stokes solution goes to an euler solution outside a boundary layer and to a solution of the prandtl equations within the boundary layer the error term is written as a sum of first order euler and prandtl corrections plus a further error term the equation for the error term is weakly nonlinear its linear part is the time dependent stokes equation this error equation is solved by inversion of the stokes equation through expressing the solution as a regular euler like part plus a boundary layer prandtl like part the main technical tool in this analysis is the abstract cauchy kowalewski theorem

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

zero viscosity limit for analytic solutions of the primitive equations the aim of this paper is to prove that the solutions of the primitive equations converge in the zero viscosity limit to the solutions of the hydrostatic euler equations we construct the solution of the primitive equations through a matched asymptotic expansion involving the solution of the hydrostatic euler equation and boundary layer correctors as the first order term and an error that we show to be o sqrt nu the main assumption is spatial analyticity of the initial datum

uniform regularity for the navier stokes equation with navier boundary condition we prove that there exists an interval of time which is uniform in the vanishing viscosity limit and for which the navier stokes equation with the navier boundary condition has a strong solution this solution is uniformly bounded in a conormal sobolev space and has only one normal derivative bounded in l this allows us to obtain the vanishing viscosity limit to the incompressible euler system from a strong compactness argument

finite time blowup for the inviscid primitive equations of oceanic and atmospheric dynamics in an earlier work we have shown the global for all initial data and all time well posedness of strong solutions to the three dimensional viscous primitive equations of large scale oceanic and atmospheric dynamics in this paper we show that for certain class of initial data the corresponding smooth solutions of the inviscid non viscous primitive equations if they exist they blow up in finite time specifically we consider the three dimensional inviscid primitive equations in a three dimensional infinite horizontal channel subject to periodic boundary conditions in the horizontal directions and with no normal flow boundary conditions on the solid top and bottom boundaries for certain class of initial data we reduce this system into the two dimensional system of primitive equations in an infinite horizontal strip with the same type of boundary conditions and then we show that for specific sub class of initial data the corresponding smooth solutions of the reduced inviscid two dimensional system develop singularities in finite time

steady prandtl boundary layer expansions over a rotating disk this paper concerns the validity of the prandtl boundary layer theory for steady incompressible navier stokes flows over a rotating disk we prove that the navier stokes flows can be decomposed into euler and prandtl flows in the inviscid limit in so doing we develop a new set of function spaces and prove several embedding theorems which capture the interaction between the prandtl scaling and the geometry of our domain

on the ill posedness of the prandtl equations in three dimensional space in this paper we give an instability criterion for the prandtl equations in three dimensional space which shows that the monotonicity condition on tangential velocity fields is not sufficient for the well posedness of the three dimensional prandtl equations in contrast to the classical well posedness theory of the two dimensional prandtl equations under the oleinik monotonicity assumption both linear stability and nonlinear stability are considered this criterion shows that the monotonic shear flow is linearly stable for the three dimensional prandtl equations if and only if the tangential velocity field direction is invariant with respect to the normal variable and this result is an exact complement to our recent work a well posedness theory for the prandtl equations in three space variables arxiv 1405 5308 2014 on the well posedness theory for the three dimensional prandtl equations with a special structure

dirichlet forms and dirichlet operators for gibbs measures of quantum unbounded spin systems essential self adjointness and log sobolev inequality for each 0 1 we consider the dirichlet form mu gamma and the associated dirichlet operator h mu gamma for the gibbs measure of quantum unbounded spin systems interacting via superstable and regular potential the gibbs measure is related to the gibbs state of the system via a functional euclidean integral procedure the configuration space for the spin systems is given by omega e mathbb z v e left omega in c left left 0 1 right mathbb r d right omega left 0 right omega left 1 right right we formulate dirichlet forms in the framework of rigged hilbert spaces which are related to the space under appropriate conditions on the potential we show that the dirichlet operator h mu left gamma right is essentially self adjoint on the domain of smooth cylinder functions we give sufficient conditions on the potential so that the corresponding gibbs measure is uniformly log concave ulc this property gives the spectral gap of the dirichlet operator h mu left gamma right at the lower end of the spectrum furthermore we prove that under the conditions of ulc the unique gibbs measure satisfies the log sobolev inequality ls we use an approximate argument used in the study of the same subjects for loop spaces which in turn is a modification of the method originally developed by s albeverio yu g kondratiev and m rockner

remarks about the inviscid limit of the navier stokes system in this paper we prove two results about the inviscid limit of the navier stokes system the first one concerns the convergence in hs of a sequence of solutions to the navier stokes system when the viscosity goes to zero and the initial data is in hs the second result deals with the best rate of convergence for vortex patch initial data in 2 and 3 dimensions we present here a simple proof which also works in the 3d case the 3d case is new

on the nonlinear instability of euler and prandtl equations in this paper we give examples of nonlinearly unstable solutions of euler equations in the whole space 2 the half space the periodic strip the strip 1 1 and the periodic torus 2 with an application to vortex sheets using the same methods we prove an instability result for prandtl type boundary layers that appear in and 2000 john wiley sons inc

the van dommelen and shen singularity in the prandtl equations abstract in 1980 van dommelen and shen provided a numerical simulation that predicted the spontaneous generation of a singularity in the prandtl boundary layer equations from a smooth initial datum for a nontrivial euler background in this paper we prove this numerical conjecture by rigorously establishing the finite time blowup of the boundary layer thickness

on the global existence of solutions to the prandtl s system abstract in this paper we establish a global existence of weak solutions to the two dimensional prandtl s system for unsteady boundary layers in the class considered by oleinik j appl math mech 30 1966 951 provided that the pressure is favourable this generalizes the local well posedness results due to oleinik 1966 mathematical models in boundary layer theory chapman hall london 1999 for the proof we introduce a viscous splitting method so that the asymptotic behaviour of the solution near the boundary can be estimated more accurately by methods applicable to the degenerate parabolic equations

local in time well posedness for compressible mhd boundary layer abstract in this paper we are concerned with the motion of electrically conducting fluid governed by the two dimensional non isentropic viscous compressible mhd system on the half plane with no slip condition on the velocity field perfectly conducting wall condition on the magnetic field and dirichlet boundary condition on the temperature on the boundary when the viscosity heat conductivity and magnetic diffusivity coefficients tend to zero in the same rate there is a boundary layer which is described by a prandtl type system under the non degeneracy condition on the tangential magnetic field instead of monotonicity of velocity by applying a coordinate transformation in terms of the stream function of magnetic field as motivated by the recent work 27 we obtain the local in time well posedness of the boundary layer system in weighted sobolev spaces

ga based meta modeling of bpn architecture for constrained approximate optimization artificial neural networks ann have been extensively used as global approximation tools in the context of approximate optimization ann traditionally minimizes the absolute difference between target outputs and approximate outputs thereby resulting in approximate optimal solutions being sometimes actually infeasible when it is used as a meta model for inequality constraint functions the paper explores the development of the modified back propagation neural network bpn based meta model that ensures the constraint feasibility of approximate optimal solution the bpn architecture is optimized via genetic algorithm ga to determine integer continuous decision parameters such as the number of hidden layers the number of neurons in a hidden layer and interconnection weights between layers in the network the verification of the proposed approach is examined by adopting a number of standard structural problems and an optical disk drive odd suspension problem finally ga based approximate optimization of suspension with optical flying head ofh is conducted to enhance the shock resistance capability in addition to dynamic characteristics

on the ill posedness of the prandtl equation the concern of this paper is the cauchy problem for the prandtl equation this problem is known to be well posed for analytic data or for data with monotonicity properties we prove here that it is linearly ill posed in sobolev type spaces the key of the analysis is the construction at high tangential frequencies of unstable quasimodes for the linearization around solutions with non degenerate critical points interestingly the strong instability is due to vicosity which is coherent with well posedness results obtained for the inviscid version of the equation a numerical study of this instability is also provided

magnetic effects on the solvability of 2d mhd boundary layer equations without resistivity in sobolev spaces abstract in this paper we are concerned with the magnetic effect on the sobolev solvability of boundary layer equations for the 2d incompressible mhd system without resistivity the mhd boundary layer is described by the prandtl type equations derived from the incompressible viscous mhd system without resistivity under the no slip boundary condition on the velocity assuming that the initial tangential magnetic field does not degenerate a local in time well posedness in sobolev spaces is proved without the monotonicity condition on the velocity field moreover we show that if the tangential magnetic field of shear layer is degenerate at one point then the linearized mhd boundary layer system around the shear layer profile is ill posed in the gevrey function space provided that the initial velocity shear flow is non degenerately critical at the same point

global well posedness of the three dimensional viscous primitive equations of large scale ocean and atmosphere dynamics in this paper we prove the global existence and uniqueness regularity of strong solutions to the three dimensional viscous primitive equations which model large scale ocean and atmosphere dynamics 1 introduction large scale dynamics of oceans and atmosphere is governed by the primitive equations which are derived from the navier stokes equations with rotation coupled to thermodynamics and salinity diffusion transport equations which account for the buoyancy forces and stratification effects under the boussinesq approximation moreover and due to the shallowness of the oceans and the atmosphere i e the depth of the fluid layer is very small in comparison to the radius of the earth the vertical large scale motion in the oceans and the atmosphere is much smaller than the horizontal one which in turn leads to modeling the vertical motion by the hydrostatic balance as a result

local existence and uniqueness of euler equation in weighted sobolev space abstract in this paper we study the existence and uniqueness of euler equation in the weighted sobolev space this is motivated by the study of inviscid limit of navier stokes equation in half plane the use of the weighted calderon zygmund inequality in the estimate of the pressure term is the improvement of our work

a lumped stress method for plane elastic problems and the discrete continuum approximation this paper proposes a rational method to approximate a plane elastic body through a latticed structure composed of truss elements the method is based on the introduction of a relaxed stress energy that allows an extension of the original problem to a larger space of admissible stress fields including stresses concentrated along lines use is made of polyhedral approximations of the airy stress function the truss analogy is employed to obtain a displacement formulation the paper includes several numerical applications of the method to sample problems a numerical convergence study and comparisons with exact solutions and standard finite element approximations

gradient dynamics of infinite point systems nonequilibrium gradient dynamics of d dimensional particle systems is investigated the interaction is given by a superstable pair potential of finite range solutions are constructed in the well defined set of locally finite configurations with a logarithmic order of energy fluctuations if the system is deterministic and d 2 then singular potentials are also allowed for stochastic models with a smooth interaction we need d 4 in order to develop some prerequisites for the theory of hydrodynamical fluctuations in equilibrium we investigate smoothness of the markov semigroup and describe some properties of its generator 0 introduction the purpose of this paper is to study existence and regularity properties of solutions to the following infinite system of stochastic differential equations consider a countable set s of d dimensional particles suspended in a fluid where the interaction is given by a pair potential u rgd 00 oo in a quasi microscopic description of such systems the effect of collisions with the particles of the fluid can be represented by uncorrelated stochastic forces and the soft resistance of the liquid medium reduces the order of the equations of motion from two to one see 13 23 and 24 for some further references configurations of these systems are countable subsets of rd such that any bounded domain contains a finite number of points only particles of a configuration will be identified by labelling points by elements of s thus a

ill posedness of the hydrostatic euler and navier stokes equations we prove that the linearization of the hydrostatic euler equations at certain parallel shear flows is ill posed the result also extends to the hydrostatic navier stokes equations with a small viscosity

on the hydrostatic approximation of the navier stokes equations in a thin strip abstract in this paper we first prove the global well posedness of a scaled anisotropic navier stokes system and the hydrostatic navier stokes system in a 2 d striped domain with small analytic data in the tangential variable then we justify the limit from the anisotropic navier stokes system to the hydrostatic navier stokes system with analytic data

dirichlet operators via stochastic analysis abstract we give sufficient conditions for essential self adjointness of symmetric differential operators dirichlet operators associated with classical dirichlet forms given by probability measures on hilbert spaces under an additional assumption of log concavity for the measures we prove the existence of a gap at the lower end of spectrum of the dirichlet operator and the ergodicity of the corresponding semi group we consider also applications to the study of stochastic dynamics in some classical lattice systems