共查询到20条相似文献,搜索用时 0 毫秒
1.
Gautam Iyer 《Communications in Mathematical Physics》2006,266(3):631-645
We prove existence and regularity of the stochastic flows used in the stochastic Lagrangian formulation of the incompressible Navier-Stokes equations (with periodic boundary conditions), and consequently obtain a C
k,α local existence result for the Navier-Stokes equations. Our estimates are independent of viscosity, allowing us to consider the inviscid limit. We show that as ν → 0, solutions of the stochastic Lagrangian formulation (with periodic boundary conditions) converge to solutions of the Euler equations at the rate of
. 相似文献
2.
Adopting the setting for the study of existence and scale locality of the energy cascade in 3D viscous flows in physical space recently introduced by the authors to 3D inviscid flows, it is shown that the anomalous dissipation is – in the case of decaying
turbulence – indeed capable of triggering the cascade which then continues ad infinitum, confirming Onsager’s predictions. 相似文献
3.
We consider a space-continuous and time-discrete polymer model for positive temperature and the associated zero temperature model of last passage percolation type. In our previous work, we constructed and studied infinite-volume polymer measures and one-sided infinite minimizers for the associated variational principle, and used these objects for the study of global stationary solutions of the Burgers equation with positive or zero viscosity and random kick forcing, on the entire real line. In this paper, we prove that in the zero temperature limit, the infinite-volume polymer measures concentrate on the one-sided minimizers and that the associated global solutions of the viscous Burgers equation with random kick forcing converge to the global solutions of the inviscid equation. 相似文献
4.
David Hoff 《Communications in Mathematical Physics》1998,192(3):543-554
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.
Received: 10 June 1997 / Accepted: 15 July 1997 相似文献
5.
A Switch Function-Based Gas-Kinetic Scheme for Simulation of Inviscid and Viscous Compressible Flows 下载免费PDF全文
Yu Sun Shu Chang Liming Yang & C. J. Teo 《advances in applied mathematics and mechanics.》2016,8(5):703-721
In this paper, a switch function-based gas-kinetic scheme (SF-GKS) is presented
for the simulation of inviscid and viscous compressible flows. With the finite
volume discretization, Euler and Navier-Stokes equations are solved and the SF-GKS
is applied to evaluate the inviscid flux at cell interface. The viscous flux is obtained by
the conventional smooth function approximation. Unlike the traditional gas-kinetic
scheme in the calculation of inviscid flux such as Kinetic Flux Vector Splitting (KFVS),
the numerical dissipation is controlled with a switch function in the present scheme.
That is, the numerical dissipation is only introduced in the region around strong shock
waves. As a consequence, the present SF-GKS can well capture strong shock waves
and thin boundary layers simultaneously. The present SF-GKS is firstly validated by
its application to the inviscid flow problems, including 1-D Euler shock tube, regular
shock reflection and double Mach reflection. Then, SF-GKS is extended to solve viscous
transonic and hypersonic flow problems. Good agreement between the present
results and those in the literature verifies the accuracy and robustness of SF-GKS. 相似文献
6.
Nader Masmoudi 《Communications in Mathematical Physics》2007,270(3):777-788
In this paper we prove two results about the inviscid limit of the Navier-Stokes system. The first one concerns the convergence
in H
s
of a sequence of solutions to the Navier-Stokes system when the viscosity goes to zero and the initial data is in H
s
. 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. 相似文献
7.
We consider a Markovian approximation, of weak coupling type, to an open system perturbation involving emission, absorption and scattering by reservoir quanta. The result is the general form for a quantum stochastic flow driven by creation, annihilation and gauge processes. A weak matrix limit is established for the convergence of the interaction-picture unitary to a unitary, adapted quantum stochastic process and of the Heisenberg dynamics to the corresponding quantum stochastic flow: the convergence strategy is similar to the quantum functional central limits introduced by Accardi, Frigerio and Lu [1]. The principal terms in the Dyson series expansions are identified and re-summed after the limit to obtain explicit quantum stochastic differential equations with renormalized coefficients. An extension of the Pulé inequalities [2] allows uniform estimates for the Dyson series expansion for both the unitary operator and the Heisenberg evolution to be obtained. 相似文献
8.
Stability Analysis of a Fully Coupled Implicit Scheme for Inviscid Chemical Non-Equilibrium Flows 下载免费PDF全文
Von Neumann stability theory is applied to analyze the stability of a fully
coupled implicit (FCI) scheme based on the lower-upper symmetric Gauss-Seidel (LU-SGS)
method for inviscid chemical non-equilibrium flows. The FCI scheme shows excellent
stability except the case of the flows involving strong recombination reactions,
and can weaken or even eliminate the instability resulting from the stiffness problem,
which occurs in the subsonic high-temperature region of the hypersonic flow field. In
addition, when the full Jacobian of chemical source term is diagonalized, the stability
of the FCI scheme relies heavily on the flow conditions. Especially in the case of high
temperature and subsonic state, the CFL number satisfying the stability is very small.
Moreover, we also consider the effect of the space step, and demonstrate that the stability
of the FCI scheme with the diagonalized Jacobian can be improved by reducing
the space step. Therefore, we propose an improved method on the grid distribution
according to the flow conditions. Numerical tests validate sufficiently the foregoing
analyses. Based on the improved grid, the CFL number can be quickly ramped up to
large values for convergence acceleration. 相似文献
9.
10.
Anthony M. Bloch Roger W. Brockett Peter E. Crouch 《Communications in Mathematical Physics》1997,187(2):357-373
In this paper we consider the geometry of Hamiltonian flows on the cotangent bundle of coadjoint orbits of compact Lie groups
and on symmetric spaces. A key idea here is the use of the normal metric to define the kinetic energy. This leads to Hamiltonian
flows of the double bracket type. We analyze the integrability of geodesic flows according to the method of Thimm. We obtain
via the double bracket formalism a quite explicit form of the relevant commuting flows and a correspondingly transparent proof
of involutivity. We demonstrate for example integrability of the geodesic flow on the real and complex Grassmannians. We also
consider right invariant systems and the generalized rigid body equations in this setting.
Received:23 July 1996 / Accepted: 16 December 1996 相似文献
11.
A kinetic equation with a relaxation time model for wave-particle collisions is considered. Similarly to the BGK-model of
gas dynamics, it involves a projection onto the set of equilibrium distributions, nonlinearly dependent on the moments of
the distribution function. Under a diffusive and low Mach number scaling the macroscopic limit is a generalization of the
incompressible Navier-Stokes equations, where the momentum equations are coupled to a diffusive equation for an energy distribution
function. By a moment approximation, this system can be related to a low Mach number model of fluid mechanics, which already
appeared in the literature. Finally, for a linearized version corresponding to Stokes flow an existence result for initial
value problems is proved. 相似文献
12.
We consider the zero viscosity limit of long time averages of solutions of damped and driven Navier-Stokes equations in . We prove that the rate of dissipation of enstrophy vanishes. Stationary statistical solutions of the damped and driven
Navier-Stokes equations converge to renormalized stationary statistical solutions of the damped and driven Euler equations.
These solutions obey the enstrophy balance. 相似文献
13.
14.
We give a general method for deducing statistical limit laws in situations where rapid decay of correlations has been established.
As an application of this method, we obtain new results for time-one maps of hyperbolic flows.
In particular, using recent results of Dolgopyat, we prove that many classical limit theorems of probability theory, such
as the central limit theorem, the law of the iterated logarithm, and approximation by Brownian motion (almost sure invariance
principle), are typically valid for such time-one maps.
The central limit theorem for hyperbolic flows goes back to Ratner 1973 and is always valid, irrespective of mixing hypotheses.
We give examples which demonstrate that the situation for time-one maps is more delicate than that for hyperbolic flows, illustrating
the need for rapid mixing hypotheses.
Received: 4 January 2002 / Accepted: 16 February 2002?Published online: 24 July 2002 相似文献
15.
Franck Sueur 《Communications in Mathematical Physics》2012,316(3):783-808
The issue of the inviscid limit for the incompressible Navier-Stokes equations when a no-slip condition is prescribed on the boundary is a famous open problem. A result by Kato (Math Sci Res Inst Publ 2:85?C98, 1984) says that convergence to the Euler equations holds true in the energy space if and only if the energy dissipation rate of the viscous flow in a boundary layer of width proportional to the viscosity vanishes. Of course, if one considers the motion of a solid body in an incompressible fluid, with a no-slip condition at the interface, the issue of the inviscid limit is as least as difficult. However it is not clear if the additional difficulties linked to the body??s dynamic make this issue more difficult or not. In this paper we consider the motion of a rigid body in an incompressible fluid occupying the complementary set in the space and we prove that a Kato type condition implies the convergence of the fluid velocity and of the body velocity as well, which seems to indicate that an answer in the case of a fixed boundary could also bring an answer to the case where there is a moving body in the fluid. 相似文献
16.
《Journal of Nonlinear Mathematical Physics》2013,20(4):549-555
Abstract We prove a uniqueness result for autonomous divergence-free systems of ODE’s in the plane and give an application to the study of water flows with vorticity. 相似文献
17.
Clayton Bjorland 《Communications in Mathematical Physics》2011,305(1):131-151
In this article we consider the physical justification of the Vortex-Wave equation introduced by Marchioro and Pulvirenti
(Mechanics, analysis and geometry: 200 years after Lagrange, North-Holland Delta Ser., Amsterdam, North-Holland, pp. 79–95,
1991), in the case of a single point vortex moving in an ambient vorticity. We consider a sequence of solutions for the Euler
equation in the plane corresponding to initial data consisting of an ambient vorticity in L
1 ∩ L
∞ and a sequence of concentrated blobs which approach the Dirac distribution. We introduce a notion of a weak solution of the
Vortex-Wave equation in terms of velocity (or primitive variables) and then show, for a subsequence of the blobs, the solutions
of the Euler equation converge in velocity to a weak solution of the Vortex-Wave equation. 相似文献
18.
Kõta Yoshioka 《Communications in Mathematical Physics》1999,205(3):501-517
Recently, Minahan, Nemeschansky, Vafa and Warner computed partition functions for N = 4 topological Yang–Mills theory on rational
elliptic surfaces. In particular they computed generating functions of Euler characteristics of SU(2)-instanton moduli spaces. In mathematics, they are expected to coincide with those of Gieseker compactifications. In this
paper, we compute Euler characteristics of these spaces and show that our results coincide with theirs. We also check the
modular property of Z
SU
(2) and Z
SO
(3) conjectured by Vafa and Witten.
Received: 8 June 1998 / Accepted: 1 February 1999 相似文献
19.
CHEN Bing-Biao 《理论物理通讯》2006,45(4)
This article gives a unified geometric interpretation of the second Matrix-AKNS hierarchies via Schr(o)dinger flows to symmetric spaces of Kahler and paraK(a)hler types. 相似文献
20.
The goal of the paper is to prove a perturbative result, concerning the uniqueness of Kerr solutions, a result which we believe
will be useful in the proof of their nonlinear stability. Following the program started in Ionescu and Klainerman (Invent.
Math. 175:35–102, 2009), we attempt to remove the analyticity assumption in the the well known Hawking-Carter-Robinson uniqueness
result for regular stationary vacuum black holes. Unlike (Ionescu and Klainerman in Invent. Math. 175:35–102, 2009), which
was based on a tensorial characterization of the Kerr solutions, due to Mars (Class. Quant. Grav. 16:2507–2523, 1999), we
rely here on Hawking’s original strategy, which is to reduce the case of general stationary space-times to that of stationary
and axi-symmetric spacetimes for which the Carter-Robinson uniqueness result holds. In this reduction Hawking had to appeal
to analyticity. Using a variant of the geometric Carleman estimates developed in Ionescu and Klainerman (Invent. Math. 175:35–102,
2009), in this paper we show how to bypass analyticity in the case when the stationary vacuum space-time is a small perturbation
of a given Kerr solution. Our perturbation assumption is expressed as a uniform smallness condition on the Mars-Simon tensor.
The starting point of our proof is the new local rigidity theorem established in Alexakis et al. (Hawking’s local rigidity
theorem without analyticity. , 2009). 相似文献