low mach number limit of full navier stokes equations in a 3d bounded domain abstract this paper studies the low mach number limit of the full compressible navier stokes equations in a three dimensional bounded domain where the velocity field and the temperature satisfy the slip boundary conditions and the neumann boundary condition respectively the uniform estimates in the mach number for the strong solutions are derived in a short time interval provided that the initial density and temperature are close to the constant states and satisfy the bounded derivative conditions thus the solutions of the full compressible navier stokes equations converge to the one of the isentropic incompressible navier stokes equations as the mach number vanishes

asymptotic of the solutions of hyperbolic equations with a skew symmetric perturbation using methods introduced by s schochet inj differential equations114 1994 476 512 we compute the first term of an asymptotic expansion of the solutions of hyperbolic equations perturbated by a skew symmetric linear operator that result is first applied to two systems describing the motion of geophysic fluids the rotating euler equations and the primitive system of the quasigeostrophic equations finally in the last part we study the slightly compressible euler equations by application of that same result

an asymptotic limit of a navier stokes system with capillary effects a combined incompressible and vanishing capillarity limit in the barotropic compressible navier stokes equations for smooth solutions is proved the equations are considered on the two dimensional torus with well prepared initial data the momentum equation contains a rotational term originating from a coriolis force a general korteweg type tensor modeling capillary effects and a density dependent viscosity the limiting model is the viscous quasi geostrophic equation for the rotated velocity potential the proof of the singular limit is based on the modulated energy method with a careful choice of the correction terms

generalized strichartz inequalities for the wave equation strichartz inequalities for the wave equation u f are estimates of the solution u of the cauchy problem for that equation in the form of space time integral norms in terms of similar norms of the inhomogeneity f and of suitable norms of the initial data

truncated dynamics and estimation of diffusion equations we study inference on continuous time processes from discrete data with a given time interval between consecutive observations and propose a modification of the sieve estimation method based on the infinitesimal generator our approach consists on truncating the initial process to improve the estimation of the eigenfunctions at the boundaries of the set of admissible values for diffusion processes nonparametric estimation of the drift and volatility are derived a prior truncation is also useful to eliminate in practice the specific dynamics of extreme risks

low mach number limit of viscous polytropic fluid flows abstract this paper studies the singular limit of the non isentropic navier stokes equations with zero thermal coefficient in a two dimensional bounded domain as the mach number goes to zero a uniform existence result is obtained in a time interval independent of the mach number provided that the initial data satisfy the bounded derivative conditions that is the time derivatives up to order two are bounded initially and navier s slip boundary condition is imposed

incompressible limit of oldroyd b fluids in the whole space abstract this paper is dedicated to the study of compressible oldroyd b model in the framework of critical spaces we first prove the local well posedness for the compressible oldroyd b model with initial data 0 1 u 0 0 b 2 1 d 2 b 2 1 d 2 1 d b 2 1 d 2 d d the global well posedness is also established provided the initial data and coupling constant are sufficiently small on the basis of this we also consider the incompressible limit problem for ill prepared initial data we prove that as the mach number tends to zero the global solution to the compressible oldroyd b fluids converges to the solution to the corresponding incompressible model in some function spaces in the meanwhile the converge rates are obtained in some sense to fulfill our proof we give a new commutator estimate

endpoint strichartz estimates we prove an abstract strichartz estimate which implies previously unknown endpoint strichartz estimates for the wave equation in dimension n 4 and the schrodinger equation in dimension n 3 three other applications are discussed local existence for a nonlinear wave equation and strichartz type estimates for more general dispersive equations and for the kinetic transport equation

the zero mach limit of compressible flows we prove that compressible navier stokes flows in two and three space dimensions converge to incompressible navier stokes flows in the limit as the mach number tends to zero no smallness restrictions are imposed on the external force the initial velocity or the time interval we assume instead that the incompressible flow exists and is reasonably smooth on a given time interval and prove that compressible flows with compatible initial data converge uniformly on that time interval our analysis shows that the essential mechanism in this process is a hyperbolic effect which becomes stronger with smaller mach number and which ultimately drives the density to a constant

low mach number limit of non isentropic magnetohydrodynamic equations in a bounded domain abstract this paper verifies the low mach number limit of the non isentropic magnetohydrodynamic equations with zero thermal coefficient in a two dimensional bounded domain with navier s slip boundary condition for velocity and perfectly conducting boundary condition for magnetic field

regular articlegeneralized strichartz inequalities for the wave equation we make a synthetic exposition of the generalized strichartz inequalities for the wave equation obtained in 6 together with the limiting cases recently obtained in 13 with as simple proofs as possible the proofs combine stationary phase estimates dyadic decompositions the hardy littlewood inequality or the holder inequality in time and abstract duality and interpolation arguments

incompressible limits and propagation of acoustic waves in large domains with boundaries we study the incompressible limit for the full navier stokes fourier system on unbounded domains with boundaries supplemented with the complete slip boundary condition for the velocity field using an abstract result of tosio kato we show that the energy of acoustic waves decays to zero on any compact subset of the physical space this in turn implies strong convergence of the velocity field to its limit in the incompressible regime

zero mach number limit for compressible flows with periodic boundary conditions we address the question of convergence to the incompressible navier stokes equations for slightly compressible viscous flows with ill prepared initial data and periodic boundary conditions the case of the whole space has been studied in an earlier paper by the author the functional setting is very close to the one used by h fujita and t kato for incompressible flows for arbitrarily large initial data we show that the compressible flow with small mach number exists as long as the incompressible one does in particular it exists globally if the corresponding incompressible solution exists for all time we further state a convergence result for the slightly compressible solution filtered by the group of acoustics introduction an engineer would hardly make a distinction between incom pressible flows and slightly compressible flows indeed incompressible navier stokes equations are usually regarded as an appropriate model for describing water in the present paper we study whether such an approximation is relevant from a mathematical viewpoint in the case of periodic boundary conditions the case of the whole space has been treated in 8 after some convenient rescaling see for instance the appendix of 16 or the introduction of 21 the equations for a slightly compressible fluid read

low mach number limit for the non isentropic navier stokes equations abstract we study the low mach number limit of the local in time solutions to the compressible navier stokes equations with zero heat conductivity coefficient as the mach number tends to zero a uniform existence result for the one dimensional initial boundary value problem is proved provided that the initial data are well prepared in the sense that the temporal derivatives up to order two are bounded initially

low mach number limit for the full compressible magnetohydrodynamic equations with general initial data abstract the low mach number limit for the full compressible magnetohydrodynamic equations with general initial data is rigorously justified in the whole space r 3 first the uniform in mach number estimates of the solutions in a sobolev space are established on a finite time interval independent of the mach number then the low mach number limit is proved by combining these uniform estimate with a theorem due to metivier and schochet 2001 45 for the euler equations that gives the local energy decay of the acoustic wave equations

low mach number limit of viscous compressible flows in the whole space this paper is devoted to the low mach number limit of weak solutions to the compressible navier stokes equations for isentropic fluids in the whole space r d d 2 or 3 this problem was investigated by p l lions and n masmoudi we present here a different approach based upon strichartz s estimates for the linear wave equation in the inviscid case which improves the convergence result and simplifies the proof we prove that the velocity field is strongly compact and converges to a global weak solution of the incompressible navier stokes equations

positive radial solutions for dirichlet problems with mean curvature operators in minkowski space abstract in this paper by using leray schauder degree arguments and critical point theory for convex lower semicontinuous perturbations of c 1 functionals we obtain existence of classical positive radial solutions for dirichlet problems of type div v 1 v 2 f x v 0 in b r v 0 on b r here b r x r n x r and f 0 r 0 r is a continuous function which is positive on 0 r 0

slow convergence to vortex patches in quasigeostrophic balance taking advantage of dispersive effects which supposes a flow extended in the whole space a sluggish convergence of the solutions of the boussinesq equations to a solution of the quasigeostrophic system when the rossby number tends to zero can be proved under weaker assumptions on the initial data than usual in particular no assumption of well preparedness is needed two examples are given both involving fields with striated potential vorticity a result of convergence to a vortex patch is deduced from one of them

the incompressible limit of solutions of the two dimensional compressible euler system with degenerating initial data using strichartz estimates it is possible to pass to the limit in the weakly compressible 2 d euler system when the mach number tends to zero even if the initial data are not uniformly smooth more precisely their norms in sobolev spaces embedded in c1 can be allowed to grow as small powers of 1 this leads to results of convergence to solutions of the incompressible euler system whose regularity is critical such as vortex patches or yudovich solutions 2000 wiley periodicals inc

incompressible limits of the navier stokes equations for all time abstract we study the asymptotic behaviors of the regular solutions to the compressible navier stokes equations for well prepared initial data for all time as the mach number tends to zero by deriving a differential inequality with certain decay property the estimates obtained in this paper are uniform both in time and mach number