higher order characteristics based method for incompressible flow computation on unstructured grids an algorithm for numerical simulation of incompressible flows on three dimensional unstructured grids is presented it is an upwind finite volume method based on the method of characteristics which is made possible with the introduction of chorin s artificial compressibility formulation flow variables are calculated along characteristics and their initial values are interpolated based on the signs of the corresponding characteristics in addition an upwind biased interpolation method of third order accuracy is used for interpolating flow variables on unstructured grids with these inherent upwinding techniques for evaluating convection fluxes at control volume surfaces no artificial viscosity is required the discretized equations are solved by an explicit multistage runge kutta time stepping scheme which is found to be efficient in terms of cpu and memory overheads a computer code has been developed using the numerical methods presented a number of test cases including two dimensional three dimensional inviscid and viscous flows have been calculated to validate the code and to evaluate the performance of the numerical algorithm

generation of viscous grids at ridges and corners an extension of lohner aiaa 93 3348 cp 1993 for the generation of high aspect ratio volume grids on surfaces with ridges and corners is presented for reynolds averaged navier stokes computations multiple point normals are introduced along ridges and corners the original technique generates a semi structured boundary layer of prismatic elements growing along point normals therefore extra degenerated faces must be introduced to take into account the multiple growth curves at ridges and corners and produce a valid topological surface triangulation the major task of the algorithm consists in recovering conformity in the surface mesh triangulation which has been lost due to the introduction of the virtual faces the procedure relies on a topological taxonomy of an arbitrary combination of concave and convex ridges each case is highlighted in detail special boundary conditions such as symmetry planes and periodic boundary conditions are also handled several complex geometries have been chosen to illustrate the proposed procedure and timings are given showing that the new module does not place any extra burden on the previous semi structured approach copyright 2008 john wiley sons ltd

asymptotic behavior for systems of nonlinear wave equations with multiple propagation speeds in three space dimensions abstract we consider the cauchy problem for systems of nonlinear wave equations with multiple propagation speeds in three space dimensions under the null condition for such systems the global existence of small amplitude solutions is known in this paper we will show that the global solution is asymptotically free in the energy sense by obtaining the asymptotic pointwise behavior of the derivatives of the solution nonetheless we can also show that the pointwise behavior of the solution itself may be quite different from that of the free solution in connection with the above results a theorem is also developed to characterize asymptotically free solutions for wave equations in arbitrary space dimensions

global existence for the einstein vacuum equations in wave coordinates we prove global stability of minkowski space for the einstein vacuum equations in harmonic wave coordinate gauge for the set of restricted data coinciding with the schwarzschild solution in the neighborhood of space like infinity the result contradicts previous beliefs that wave coordinates are unstable in the large and provides an alternative approach to the stability problem originally solved for unrestricted data in a different gauge and with a precise description of the asymptotic behavior at null infinity by d christodoulou and s klainerman

bounded query classes polynomial time machines having restricted access to an np oracle are investigated restricted access means that the number of queries to the oracle is restricted or the way in which the queries are made is restricted e g queries made during truth table reductions very different kinds of such restrictions result in the same or comparable complexity classes in particular the class p text np o log n can be characterized in very different ways furthermore the boolean hierarchy is generalized in such a way that it is possible to characterize p text np and p text np o log n in terms of the generalization

almost global existence for 2 d incompressible isotropic elastodynamics author s lei z sideris tc zhou y abstract 2015 american mathematical society we consider the cauchy problem for 2 d incompressible isotropic elastodynamics standard energy methods yield local solutions on a time interval 0 t for initial data of the form u0 where t depends only on some sobolev norm of u0 we show that for such data there exists a unique solution on a time interval 0 exp t provided that is sufficiently small this is achieved by careful consideration of the structure of the nonlinearity the incompressible elasticity equation is inherently linearly degenerate in the isotropic case in other words the equation satisfies a null condition this is essential for time decay estimates the pressure which arises as a lagrange multiplier to enforce the incompressibility constraint is estimated in a novel way as a nonlocal nonlinear term with null structure the proof employs the generalized energy method of klainerman enhanced by weighted l2 estimates and the ghost weight introduced by alinhac

temps de vie des solutions regulieres des equations d euler compressibles axisymetriques en dimension deux nous considerons le systeme des equations d euler isentropiques en dimension deux pour des donnees initiales invariantes par rotation et perturbations de taille e d un etat de repos on etablit un equivalent du temps de viet e de la solution classique lim 2 t 2 de plus on donne pour t leqq frac a 2 varepsilon 2 a tau une estimation de la vraie solution en calculant la taille de son ecart a une solution approchee construite dans un precedent travail

local existence of solutions for the initial boundary value problem of the nonlinear elastodynamic system outside a domain abstract in this paper we deal with the mixed initial boundary value problem of dirichlet type for the nonlinear elastodynamic system outside a domain the local existence of solutions to this problem is proved by iteration

global well posedness for the three dimensional simplified inertial ericksen leslie systems near equilibrium abstract we study a simplified inertial ericksen leslie system for the nematic liquid crystal flow which can be viewed as a system coupling navier stokes equations and wave map equations we prove the global existence of classical solution with initial data near equilibrium

global existence of null form wave equations on small asymptotically euclidean manifolds abstract we prove the global existence of the small solutions to the cauchy problem for quasilinear wave equations satisfying the null condition on r 3 g where the metric g is a small perturbation of the flat metric and approaches the euclidean metric like 1 x 2 2 with 1 global and almost global existence for systems without the null condition are also discussed for certain small time dependent perturbations of the flat metric in appendix a

global existence for systems of quasilinear wave equations in 1 4 dimensions abstract hormander proved global existence of solutions for sufficiently small initial data for scalar wave equations in 1 4 dimensions of the form u q u u u where q vanishes to second order and u 2 q 0 0 0 0 without the latter condition only almost global existence may be guaranteed the first author and sogge considered the analog exterior to a star shaped obstacle both results relied on writing the lowest order terms u u 1 2 u 2 and as such do not immediately generalize to systems the current study remedies such and extends both results to the case of multiple speed systems

almost global existence for quasilinear wave equations in waveguides with neumann boundary conditions in this paper we prove almost global existence of solutions to certain quasilinear wave equations with quadratic nonlinearities in infinite homogeneous waveguides with neumann boundary conditions we use a galerkin method to expand the laplacian of the compact base in terms of its eigenfunctions for those terms corresponding to zero modes we obtain decay using analogs of estimates of klainerman and sideris for the nonzero modes estimates for klein gordon equations which provide better decay are available

uniform bound of sobolev norms of solutions to 3d nonlinear wave equations with null condition abstract this article concerns the time growth of sobolev norms of classical solutions to the 3d quasi linear wave equations with the null condition given initial data in h s h s 1 with compact supports the global well posedness theory has been established independently by klainerman 13 and christodoulou 3 respectively for a relatively large integer s however the highest order sobolev energy namely the h s energy of solutions may have a logarithmic growth in time in this paper we show that the h s energy of solutions is also uniformly bounded for s 5 the proof employs the generalized energy method of klainerman enhanced by weighted l 2 estimates and the ghost weight introduced by alinhac

global solutions for nonlinear wave equations with localized dissipations in exterior domains abstract the cauchy problem for nonlinear wave equations with localized dissipation is considered in exterior domains outside of compact obstacles in three spatial dimensions under the null conditions for the quadratic nonlinear terms the global solutions are shown for sufficiently small data the solutions which have different propagation speeds are considered

more complicated questions about maxima and minima and some closures of np abstract starting from np complete problems defined by questions of the kind max m and min m we consider problems defined by more complicated questions about these maxima and minima as for example max m min m and is max odd this continues a work started by papadimitriou and yannakakis 1982 it is shown that these and other problems are complete in certain subclasses of the boolean closure of np and other classes in the interesting area below the class p 2 of the polynomial time hierarchy special methods are developed to prove such completeness results for this it is necessary to establish some properties of the classes in question which might be interesting in their own right

complexity analysis of a unifying algorithm for model checking interval temporal logic abstract model checking mc for halpern and shoham s interval temporal logic hs has been recently shown to be decidable an intriguing open question is its exact complexity for full hs it is at least expspace hard and the only known upper bound which exploits an abstract representation of kripke structure paths descriptor is non elementary in this paper we provide a uniform framework to mc for full hs and meaningful fragments of it with a specific type of descriptor for each fragment then we devise a general mc alternating algorithm parameterized by the descriptor s type which has a polynomially bounded number of alternations and whose running time is bounded by the length of minimal representatives of descriptors certificates we analyze its complexity and give tight bounds on the length of certificates for two types of descriptor we obtain exponential upper and lower bounds for the other ones we provide non elementary lower bounds

on almost global existence for nonrelativistic wave equations in 3d almost global solutions are constructed to three dimensional quadratically nonlinear wave equations the proof relies on generalized energy estimates and a new decay estimate the method applies to equations that are only classically invariant such as the nonlinear system of hyperelasticity 1996 john wiley sons inc

resonance type behaviour in a system of nonlinear wave equations consider the cauchy problem for a system of two wave equations in r3 c12 t2u1 u1 u 1 u 2c22 t2 u2 u 1 u 2 where prime stands for any partial derivative in space or time variables if initial data is small in a suitable norm the following phenomenon occurs if c1 c2 the system possesses smooth solutions for all t 0 whereas if c1 c2 the solutions of the system might blowup the result is proved for a more general form of the above system in the case of a three space dimension also a similar result is proved for two space dimensions

space time l 2 estimates for elastic waves and applications abstract we establish a kind of weighted space time l 2 estimate which belongs to keel smith sogge type estimates for perturbed linear elastic wave equations in r n n 3 we also apply this estimate to give an alternative and short proof for john s almost global existence theorem for 3 d nonlinear elastic waves john 1988 10 and show the global existence of small smooth solutions for nonlinear elastic waves in high space dimensions n 4

delayed singularity formation in 2d compressible flow the initial value problem for the compressible euler equations in two space dimensions is studied of interest is the lifespan of classical solutions with initial data that is a small perturbation from a constant state the approach taken is to regard the compressible solution as a nonlinear superposition of an underlying incompressible flow and an irrotational compressible flow this viewpoint yields an improvement for the lifespan over that given by standard existence theory the estimate for the lifespan is further improved when the initial data possesses certain symmetry in the case of rotational symmetry a result of s alinhac is reconsidered the approach is also applied to the study of the incompressible limit the analysis combines energy and decay estimates based on vector fields related to the natural invariance of the equations 0 introduction the compressible euler equations comprise a nonlinear symmetric hyperbolic system of pde s that model ideal fluid flow the charac teristic wave speeds of this system are given by the fluid velocity and the local sound speed the two wave families associated to these speeds may be con sidered separately hydrodynamical waves are described by the incompressible euler equations while acoustical waves are approximated by the linear wave equation or more precisely by the compressible euler equations with irrotational fluid velocity this paper attempts to use the nonlinear superposition of these two flows to study the long time behavior of small amplitude disturbances in two dimensional compressible fluid flow consider the initial value problem for the compressible euler equations in two or three space dimensions with smooth initial data which is a small perturbation of amplitude e from a constant state the life span is defined as the largest time interval on which there exists a classical solution to the initial value problem from the theory of symmetric hyperbolic systems 6 8 the life span is at least 0 e results on formation of singularities show that the life span of a classical solution is no better than 0 e2 in 2d 16 and o exp l 2 in 3d 17 in this paper we extend the length of the life span under various assumptions on the initial data in two space dimensions the simplest case is the one in which the initial fluid velocity is irrotational that is its curl is zero the compressible euler equations then behave much the same as scalar nonlinear wave equations this can readily be guessed by writing the velocity as the gradient of a potential although we will not use this approach here we shall see in theorem 2 that the life span of 2d irrotational

global existence of classical solutions to the cauchy problem for a kind of quasilinear hyperbolic system abstract this paper deals with the cauchy problem for a kind of quasilinear hyperbolic system with the linear elastodynamic system as its principal part and the nonlinear terms depending on quadratic terms of the first derivatives of u a system of new null conditions is given by which the author shows the global existence of the problem

global smooth axisymmetric solutions to 2d compressible euler equations of chaplygin gases with non zero vorticity abstract for 2d compressible isentropic euler equations of polytropic gases s alinhac establishes that the axisymmetric smooth solution blows up in the present paper for 2d compressible isentropic euler equations of chaplygin gases we show that the small perturbed smooth solution exists globally when the rotationally invariant initial data are a perturbation of size e 0 of a rest state near the light cone 2d euler equations of chaplygin gases can be transformed into a second order quasilinear wave equation which satisfies both the null conditions this will lead to that the corresponding second order quasilinear wave equation admits a global smooth solution near the light cone however away from the light cone the hydrodynamical waves have no decay in time and strongly affect the related acoustical waves by introducing a nonlinear ode we can distinguish the fast decay part and non decay part so that the global energy estimates are derived

np trees and carnap s modal logic in this paper we consider problems and complexity classes definable by interdependent queries to an oracle in np how the queries depend on each other is specified by a directed graph g we first study the class of problems where g is a general dag and show that this class coincides with d p 2 we then consider the class where g is a tree our main result states that this class is identical to p np o log n the class of problems solvable in polynomial time with a logarithmic number of queries to an oracle in np this result has interesting applications in the fields of modal logic and artificial intelligence in particular we show that the following problems are all p np o log n complete validity checking of formulas in carnap s modal logic checking whether a formula is almost surely valid over finite structures in modal logics k t and s4 a problem recently considered by halpern and kapron 1992 and checking whether a formula belongs to the stable set of beliefs generated by a propositional theory we generalize the case of dags to the case where g is a general possibly cyclic directed graph of np oracle queries and show that this class corresponds to p p 2 we show that such graphs are easily expressible in autoepistemic logic finally we generalize our complexity results to higher classes of the polynomial time hierarchy

on the global existence and stability of a multi dimensional supersonic conic shock wave we establish the global existence and stability of a three dimensional supersonic conic shock wave for a compactly perturbed steady supersonic flow past an infinitely long circular cone with a sharp angle the flow is described by a 3 d steady potential equation which is multi dimensional quasilinear and hyperbolic with respect to the supersonic direction making use of the geometric properties of the pointed shock surface together with the rankine hugoniot conditions on the conic shock surface and the boundary condition on the surface of the cone we obtain a global uniform weighted energy estimate for the nonlinear problem by finding an appropriate multiplier and establishing a new hardy type inequality on the shock surface based on this we prove that a multi dimensional conic shock attached to the vertex of the cone exists globally when the mach number of the incoming supersonic flow is sufficiently large moreover the asymptotic behavior of the 3 d supersonic conic shock solution which is shown to approach the corresponding background shock solution in the downstream domain for the uniform supersonic constant flow past the sharp cone is also explicitly given

model checking for fragments of the interval temporal logic hs at the low levels of the polynomial time hierarchy abstract some temporal properties of reactive systems such as actions with duration and temporal aggregations which are inherently interval based can not be properly expressed by the standard point based temporal logics ltl ctl and ctl as they give a state by state account of system evolution conversely interval temporal logics which feature intervals instead of points as their primitive entities naturally express them we study the model checking mc problem for halpern and shoham s modal logic of time intervals hs interpreted on kripke structures under the homogeneity assumption hs is the best known interval based temporal logic which has one modality for each of the 13 ordering relations between pairs of intervals allen s relations apart from equality we focus on mc for some hs fragments featuring modalities for a subset of allen s relations meet met by started by and finished by showing that it is in p np additionally we provide some complexity lower bounds to the problem

model checking for fragments of halpern and shoham s interval temporal logic based on track representatives abstract model checking allows one to automatically verify a specification of the expected properties of a system against a formal model of its behavior generally a kripke structure point based temporal logics such as ltl ctl and ctl that describe how the system evolves state by state are commonly used as specification languages they proved themselves quite successful in a variety of application domains however properties constraining the temporal ordering of temporally extended events as well as properties involving temporal aggregations which are inherently interval based can not be properly dealt with by them interval temporal logics itls that take intervals as their primitive temporal entities turn out to be well suited for the specification and verification of interval properties of computations we interpret all the tracks of a kripke structure as computation intervals in this paper we study the model checking problem for some fragments of halpern and shoham s modal logic of time intervals hs hs features one modality for each possible ordering relation between pairs of intervals the so called allen s relations first we describe an expspace model checking algorithm for the hs fragment of allen s relations meets met by starts started by and finishes which exploits the possibility of finding for each track of unbounded length an equivalent bounded length track representative while checking a property it only needs to consider tracks whose length does not exceed the given bound then we prove the model checking problem for such a fragment to be pspace hard finally we identify other well behaved hs fragments which are expressive enough to capture meaningful interval properties of systems such as mutual exclusion state reachability and non starvation and whose computational complexity is less than or equal to that of ltl

the lifespan for nonlinear wave equations with multiple propagation speeds in 3d abstract in this paper we consider the cauchy problem for systems of nonlinear wave equations with multiple propagation speeds in three space dimensions on the basis of some klainerman sideris type weighted estimates we get the lifespan of small amplitude solutions for systems with nonlinearities depending on both the unknown functions and their derivatives

two remarks on the power of counting the relationship between the polynomial hierarchy and valiant s class p is at present unknown we show that some low portions of the polynomial hierarchy namely deterministic polynomial algorithms using an np oracle at most a logarithmic number of times can be simulated by one p computation we also show that the class of problems solvable by polynomial time nondeterministic turing machines which accept whenever there is an odd number of accepting computations is idempotent that is closed under usage of oracles from the same class

on nonlinear elastic waves in 2 d abstract for the cauchy problem of 2 d nonlinear elastic waves of isotropic homogeneous and hyperelastic materials satisfying null conditions assuming the smallness of h 3 r 2 h 2 r 2 norm and the boundedness of h 4 r 2 h 3 r 2 norm for radially symmetric initial data we show the global existence of classical solutions similar results for exterior domain problems are also proved

nonresonance and global existence of prestressed nonlinear elastic waves this article considers the existence of global classical solutions to the cauchy problem in nonlinear elastodynamics the unbounded elastic medium is assumed to be homogeneous isotropic and hyperelastic as in the theory of 3d nonlinear wave equations in three space dimensions global existence hinges on two basic assumptions first the initial deformation must be a small displacement from equilibrium in this case a prestressed homogeneous dilation of the reference conflguration and equally important the nonlinear terms must obey a type of nonresonance or null condition the omission of either of these assumptions can lead to the breakdown of solutions in flnite time in particular nonresonance complements the genuine nonlinearity condition of f john under which arbitrarily small spherically symmetric displacements develop singularities although one expects this to carry over to the nonsymmetric case as well 4 john also showed that small solutions exist almost globally 5 see also 10 formation of singularities for large displacements was illustrated by tahvildar zadeh 16 the nonresonance condition introduced here represents a substantial improvement over our previous work on this topic 13 to explain the difierence roughly our earlier version of the null condition forced the cancellation of all nonlinear wave interactions to flrst order along the characteristic cones here only the cancellation of nonlinear wave interactions among individual wave families is required the di culty in realizing this weaker version is that the decomposition of elastic waves into their longitudinal and transverse components involves the nonlocal helmholtz projection which is ill suited to nonlinear analysis however our decay estimates make clear that only the leading contribution of the resonant interactions along the characteristic cones is potentially dangerous and this permits the usage of approximate local decompositions

almost global existence to nonlinear wave equations in three space dimensions on considere l existence a t grand de solutions de petite amplitude pour des equations d onde d ordre 2 non lineaires a 4 dimensions d espace temps

the lifespan of a class of smooth spherically symmetric solutions of the compressible euler equations with variable entropy in three space dimensions we consider smooth three dimensional spherically symmetric eulerian flows of ideal polytropic gases with variable entropy whose initial data are obtained by adding a small smooth perturbation with compact support to a constant state under a natural assumption we obtain precise information on the asymptotic behavior of their lifespan when the size of the initial perturbation tends to 0 this is achieved by the construction and estimate of a suitable approximate flow

global existence for dirichlet wave equations with quadratic nonlinearities in high dimensions we prove global existence of solutions to quasilinear wave equations with quadratic nonlinearities exterior to nontrapping obstacles in spatial dimensions 4 and higher this generalizes a result of shibata and tsutsumi in spatial dimensions greater than or equal to 6 the technique of proof would allow for more complicated geometries provided that an appropriate local energy decay exists for the associated linear wave equation

a vector field method for massless relativistic transport equations and applications abstract in this article we present a vector field method for the study of solutions to massless relativistic transport equations compared to 10 we remove the lorentz boosts of the commutation vector fields and we prove a new functional inequality in order to derive pointwise decay estimates on the solutions it makes our method more suitable for the study of systems coupling a massless vlasov equation with an equation which has a different speed of propagation we also believe that our approach can be adapted more easily to the context of curved backgrounds in the second part of this paper we apply our method in order to derive sharp decay estimates on the spherically symmetric small data solutions of the relativistic massless vlasov poisson system no compact support assumption is required on the data and in particular the initial decay in the velocity variable is optimal in order to compensate the slow decay rate of the particle density near the light cone we take advantage of the null structure of the equations

on truth table reducibility to sat we show that polynomial time truth table reducibility via boolean circuits to sat is the same as logspace truth table reducibility via boolean formulas to sat and the same as logspace turing reducibility to sat in addition we prove that a constant number of rounds of parallel queries to sat is equivalent to one round of parallel queries we give an oracle relative to which 2p is not equal to the class of predicates polynomial time truth table reducible to sat

three dimensional unstructured adaptive multigrid scheme for the navier stokes equations a solution adaptive multigrid scheme for solving the three dimensional navier stokes equations on unstructured meshes is presented the algorithm solves the equations on a fully unstructured mesh of tetrahedral elements using a multigrid time marching scheme the initial unstructured mesh is successively refined based on gradients in the flow solution with the multigrid levels being determined by the refinement procedure important issues related to solving viscous flows on unstructured meshes are discussed these include calculation of the viscous stress terms in a manner that prevents wiggles calculation of the time steps to include both inviscid and viscous effects numerical smoothing considerations minimization of computer storage requirements and implementation of the k e turbulence model solutions are presented for several examples of industrial importance that illustrate the potential of the method including transonic flow about an aircraft engine nacelle and in both rotating and nonrotating turbomachinery passages

local existence of solutions for the neumann problem of the nonlinear elastodynamic system outside a domain abstract in this paper we study the mixed initial boundary value problem of neumann type for the nonlinear elastic wave equation outside a domain the local existence of solutions to this problem is proved by iteration to get this result we prove the existence of solutions for the second order linear hyperbolic system with variable coefficients in sobolev spaces outside of a domain by using linear evolution operators and integro differential equations

a three dimensional parametric mesher with surface boundary layer capability abstract a novel parametric surface meshing technique is presented its distinctive feature relies on successive approximations of the cad geometry through a hierarchical process where geometric information is gathered incrementally a detailed review of zero and first order surface approximations and their impact on parametric surface meshing algorithms is performed the proposed approach emphasizes the use of three dimensional information in order to be as independent as possible of the parametrization to overcome limitations of meshing purely in the parametric plane the presented technique includes semi structured boundary layer surface mesh generation which is a critical capability for accurate solutions to flows around geometries that have leading edge features numerous examples illustrate the method s robustness and ability to high quality meshes for complex cad geometries

global existence for three dimensional incompressible isotropic elastodynamics the existence of global in time classical solutions to the cauchy problem for incompressible nonlinear isotropic elastodynamics for small initial displacements is proved the generalized energy method is used to obtain strong dispersive estimates that are needed for long time stability this requires the use of weighted local decay estimates for the linearized equations which are obtained as a special case of a new general result for certain isotropic symmetric hyperbolic systems in addition the pressure that arises as a lagrange multiplier to enforce the incompressibility constraint is estimated as a nonlinear term the incompressible elasticity equations are inherently linearly degenerate in the isotropic case i e the equations satisfy a null condition necessary for global existence in three dimensions c 2007 wiley periodicals inc

global solutions for incompressible viscoelastic fluids we prove the existence of both local and global smooth solutions to the cauchy problem in the whole space and the periodic problem in the n dimensional torus for the incompressible viscoelastic system of oldroyd b type in the case of near equilibrium initial data the results hold in both two and three dimensional spaces the results and methods presented in this paper are also valid for a wide range of elastic complex fluids such as magnetohydrodynamics liquid crystals and mixture problems

global solutions of nonlinear wave equations in time dependent inhomogeneous media we consider the problem of small data global existence for a class of semilinear wave equations with null condition on a lorentzian background mathbb r 3 1 g with a time dependent metric g coinciding with the minkowski metric outside the cylinder t x x leq r we show that the small data global existence result can be reduced to two integrated local energy estimates and demonstrate that these estimates work in the particular case when g is merely c1 close to the minkowski metric one of the novel aspects of this work is that it applies to equations on backgrounds which do not settle to any particular stationary metric

global existence for systems of wave equations with nonresonant nonlinearities and null forms abstract we consider the cauchy problem for systems of nonlinear wave equations with different propagation speeds in three space dimensions we prove global existence of small amplitude solutions for systems with some nonresonant nonlinearities which may depend on both of the unknowns and their derivatives our method here can be also adopted to treat the null forms

global existence for nonlinear elastic waves in high space dimensions abstract in georgiev et al 2005 the authors proved the global existence of solutions to the cauchy problem of nonlinear elastic waves with memory for space dimensions n 3 in this manuscript we show that in high space dimensions n 4 even without such memory effect global solutions can be also constructed the main tool we used is the vector fields method adapted to elastic waves in sideris s work sideris 2000

global solutions to repulsive hookean elastodynamics the global existence of classical solutions to the three dimensional repulsive hookean elastodynamics around an equilibrium is considered by linearization and hodge s decomposition the compressible part of the velocity the density and the compressible part of the transpose of the deformation gradient satisfy klein gordon equations with speed sqrt 2 while the incompressible parts of the velocity and of the transpose of the deformation gradient satisfy wave equations with speed one the space time resonance method combined with the vector field method is used in a novel way to obtain the decay of the solution and hence global existence

almost global existence for quasilinear wave equations in three space dimensions this article studies almost global existence for solutions of quadratically quasi linear systems of wave equations in three space dimensions the approach here uses only the classical invariance of the wave operator under translations spatial rotations and scaling using these techniques we can handle wave equations in minkowski space or dirichlet wave equations in the exterior of a smooth star shaped obstacle we can also apply our methods to systems of quasilinear wave equations having different wave speeds this extends our work 11 for the semilinear case previous almost global ex istence theorems for quasilinear equations in three space dimensions were for the non obstacle case in 9 john and klainerman proved almost global existence on minkowski space for quadratic quasilinear equations using the lorentz invariance of the wave operator in addition to the symmetries listed above subsequently in 14 klainerman and sideris obtained the same result for a class of quadratic divergence form nonlinearities without relying on lorentz invariance this line of thought was refined and applied to prove global in time results for null form equa tions related to the theory of elasticity in sideris 22 23 and for multiple speed systems of null form quasilinear equations in sideris and tu 24 and yokoyama 29 the main difference between our approach and the earlier ones is that we ex ploit the 0 x 1 decay of solutions of wave equations with sufficiently decaying initial data as much as we involve the stronger 0 t l decay here of course x x x2 x is the spatial component and t the time component of a space time vector t x g m x e3 establishing 0 x 1 decay is considerably easier and can be achieved using only the invariance with respect to translations and spatial rotation a weighted l2 space time estimate for inhomogeneous wave equations proposition 3 1 below from 11 is important in making the spatial decay useful for the long time existence argument for semilinear systems one can show almost global existence from small data using only this spatial decay 11 for quasilinear systems however we also have to show that both first and second derivatives of u decay like 1 t fortunately we can do this using a variant of some l1 l estimates of john h rmander

global smooth solutions of 3 d null form wave equations in exterior domains with neumann boundary conditions abstract the paper is devoted to investigating long time behavior of smooth small data solutions to 3 d quasilinear wave equations outside of compact convex obstacles with neumann boundary conditions concretely speaking when the surface of a 3 d compact convex obstacle is smooth and the quasilinear wave equation fulfills the null condition we prove that the smooth small data solution exists globally provided that the neumann boundary condition on the exterior domain is given one of the main ingredients in the current paper is the establishment of local energy decay estimates of the solution itself as an application of the main result the global stability to 3 d static compressible chaplygin gases in exterior domain is shown under the initial irrotational perturbation with small amplitude

space time resonances and the null condition for first order systems of wave equations in this manuscript we prove global existence and linear asymptotic behavior of small solutions to nonlinear wave equations we assume that the quadratic part of the nonlinearity satisfies a nonresonance condition that is a generalization of the null condition given by klainerman 2013 wiley periodicals inc

global existence for three dimensional incompressible isotropic elastodynamics via the incompressible limit the existence of global in time classical solutions to the cauchy problem for incompressible nonlinear isotropic elastodynamics for small initial displacements is proved solutions are constructed via approximation by slightly compressible materials the energy for the approximate solutions remains uniformly bounded on a time scale that goes to infinity as the material approaches incompressibility a necessary component to the long time existence of the approximating solution is a null or linear degeneracy condition inherent in the isotropic case which limits the quadratic interaction of the shear waves the proof combines energy and decay estimates based on commuting vector fields and a compactness argument 2004 wiley periodicals inc

equations d ondes quasilineaires et estimations de strichartz dans cet article notre but est de resoudre des equations d ondes quasilineaires pour des donnees initiales moins regulieres que ce qu imposent les methodes d energie ceci impose de demontrer des estimees de type strichartz pour des operateurs d ondes a coefficients seulement lipschitziens

global shock waves for the supersonic flow past a perturbed cone we prove the global existence of a shock wave for the stationary supersonic gas flow past an infinite curved and symmetric cone the flow is governed by the potential equation as well as the boundary conditions on the shock and the surface of the body it is shown that the solution to this problem exists globally in the whole space with a pointed shock attached at the tip of the cone and tends to a self similar solution under some suitable conditions our analysis is based on a global uniform weighted energy estimate for the linearized problem combining this with the local existence result of chen li 1 we establish the global existence and decay rate of the solution to the nonlinear problem

semistructured mesh generation for three dimensional navier stokes calculations to mesh complex geometries efficiently is the authors view that a fully unstructured mesh generation technique holds the most promise there are many papers detailing mesh generation and flow solutions for inviscid flows on unstructured meshes however the computation of viscous flows on unstructured meshes is a relatively new area of research to accurately and efficiently compute viscous flows highly stretched cells aligned in the proper direction are required in the viscous layers many of the currently available unstructured mesh generators provide at most a limited ability to create these cells in the current work a method that builds layers of highly stretched prismatic cells on an existing unstructured surface triangulation is described the outer surface of this inflated triangulation provides a natural starting point for the advancing front algorithm used to fill the interior with tetrahedra care is taken to limit the possibility of a crossed over mesh in concave geometrical regions if the mesh does cross over then the offending cells are removed the combined algorithm of surface inflation and advancing front is demonstrated on a range of internal and external flow test cases a limited number of flow solutions are also presented

almost global existence for the initial value problem of nonlinear elastodynamic system the authors deal with the cauchy problem with small initial data for the nonlinear elastodynamic system the almost global existence of solution to this problem is proved in a simpler way and a lower bound for the lifespan of solutions is given

a note on quasilinear wave equations in two space dimensions ii almost global existence of classical solutions abstract we give an alternative proof of alinhac s almost global existence result for the cauchy problem of quasilinear wave equations with quadratic nonlinearity satisfying the null condition in 2 d s alinhac 2001 3 the main innovation of our proof is that the lorentz boost operator is not employed in the generalized energy estimates

the complexity of propositional linear temporal logics the complexity of satisfiability and determination of truth in a particular finite structure are considered for different propositional linear temporal logics it is shown that these problems are np complete for the logic with f and are pspace complete for the logics with f x with u with u s x operators and for the extended logic with regular operators given by wolper

the null condition for quasilinear wave equations in two space dimensions ii we consider quasilinear wave equations with small data of size e in two space dimensions assuming the null condition is satisfied we proved in a previous paper the conjectured large time existence result in this paper using the geometric blowup techniques introduced in our previous work we prove that under generic conditions on the data blowup does occur at the specified time more precisely the blowup can be described as a geometric blowup of cusp type uniformly in e in appropriate variables taking advantage of the techniques introduced in the paper we also prove the blowup result for the technically similar case of quasilinear wave equations without null condition in three space dimensions

global solutions of nonlinear hyperbolic equations for small initial data on considere des systemes quasilineaires d equations hyperboliques d ordre 2 qui sont des deformations non lineaires de l equation d onde on etudie l existence globale et le comportement asymptotique des solutions du probleme de cauchy quand la donnee initiale est suffisamment petite

global existence of null form wave equations in exterior domains we provide a proof of global existence of solutions to quasilinear wave equations satisfying the null condition in certain exterior domains in particular our proof does not require estimation of the fundamental solution for the free wave equation we instead rely upon a class of keel smith sogge estimates for the perturbed wave equation using this a notable simplification is made as compared to previous works concerning wave equations in exterior domains one no longer needs to distinguish the scaling vector field from the other admissible vector fields

uniform decay estimates and the lorentz invariance of the classical wave equation on etudie le comportement asymptotique des solutions de u 0 ou t 2 1 2 n 2 pour des conditions initiales u 0 u t g x en t 0 avec g reguliere a support compact dans r n

a folding unfolding algorithm for the construction of semi structured layers in hybrid grid generation abstract a method is presented for generating semi structured layers in hybrid grids suitable for high reynolds number flow simulations it can produce superior quality grids around convex and concave ridges of the domain compared to a standard prismatic or advancing layers generator in a first step hybrid quadrilateral triangular grids are employed to cluster the surface grid towards sharp corners and ridges starting from this surface grid as an initial front for the volume grid generation a prismatic and hexahedral layers generation technique is used containing degenerate faces to add or remove elements in convex or concave areas of the geometry respectively the method can automatically create structured like grids in concave gaps and better discretize the space around convex ridges to improve overall accuracy the final grid remains conforming to not complicate the solver and post processing requirements several examples illustrate the application of the method

global existence for a model of inhomogeneous incompressible elastodynamics in 2d abstract in this paper we investigate a model of incompressible isotropic inhomogeneous elastodynamics in two space dimensions inspired by lei in 18 we prove the global existence for this cauchy problem with sufficiently small initial displacement and small density disturbance around constant