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1.
We study the low Mach number asymptotic limit for solutions to the full Navier–Stokes–Fourier system, supplemented with ill-prepared
data and considered on an arbitrary time interval. Convergencetowards the incompressible Navier–Stokes equations is shown. 相似文献
2.
We establish a Navier–Stokes–Fourier limit for solutions of the Boltzmann equation considered over any periodic spatial domain
of dimension two or more. We do this for a broad class of collision kernels that relaxes the Grad small deflection cutoff
condition for hard potentials and includes for the first time the case of soft potentials. Appropriately scaled families of
DiPerna–Lions renormalized solutions are shown to have fluctuations that are compact. Every limit point is governed by a weak
solution of a Navier–Stokes–Fourier system for all time. 相似文献
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4.
Imran Akhtar Ali H. Nayfeh Calvin J. Ribbens 《Theoretical and Computational Fluid Dynamics》2009,23(3):213-237
Proper orthogonal decomposition (POD) has been used to develop a reduced-order model of the hydrodynamic forces acting on
a circular cylinder. Direct numerical simulations of the incompressible Navier–Stokes equations have been performed using
a parallel computational fluid dynamics (CFD) code to simulate the flow past a circular cylinder. Snapshots of the velocity
and pressure fields are used to calculate the divergence-free velocity and pressure modes, respectively. We use the dominant
of these velocity POD modes (a small number of eigenfunctions or modes) in a Galerkin procedure to project the Navier–Stokes
equations onto a low-dimensional space, thereby reducing the distributed-parameter problem into a finite-dimensional nonlinear
dynamical system in time. The solution of the reduced dynamical system is a limit cycle corresponding to vortex shedding.
We investigate the stability of the limit cycle by using long-time integration and propose to use a shooting technique to
home on the system limit cycle. We obtain the pressure-Poisson equation by taking the divergence of the Navier–Stokes equation
and then projecting it onto the pressure POD modes. The pressure is then decomposed into lift and drag components and compared
with the CFD results. 相似文献
5.
We consider the asymptotic limit for the complete Navier–Stokes–Fourier system as both Mach and Froude numbers tend to zero.
The limit is investigated in the context of weak variational solutions on an arbitrary large time interval and for the ill-prepared
initial data. The convergence to the Oberbeck–Boussinesq system is shown.
相似文献
6.
Juhi Jang 《Archive for Rational Mechanics and Analysis》2010,195(3):797-863
We establish the local-in-time well-posedness of strong solutions to the vacuum free boundary problem of the compressible
Navier–Stokes–Poisson system in the spherically symmetric and isentropic motion. Our result captures the physical vacuum boundary
behavior of the Lane–Emden star configurations for all adiabatic exponents
g < \frac65{\gamma < \frac{6}{5}} . 相似文献
7.
Dorin Bucur Eduard Feireisl Šárka Nečasová 《Journal of Mathematical Fluid Mechanics》2008,10(4):554-568
We consider a stationary Navier–Stokes flow in a bounded domain supplemented with the complete slip boundary conditions. Assuming
the boundary of the domain is formed by a family of unidirectional asperities, whose amplitude as well as frequency is proportional
to a small parameter ε, we shall show that in the asymptotic limit the motion of the fluid is governed by the same system
of the Navier–Stokes equations, however, the limit boundary conditions are different. Specifically, the resulting boundary
conditions prevent the fluid from slipping in the direction of asperities, while the motion in the orthogonal direction is
allowed without any constraint.
The work of Š. N. supported by Grant IAA100190505 of GA ASCR in the framework of the general research programme of the Academy
of Sciences of the Czech Republic, Institutional Research Plan AV0Z10190503. 相似文献
8.
We study the vanishing viscosity limit of the compressible Navier–Stokes equations to the Riemann solution of the Euler equations
that consists of the superposition of a shock wave and a rarefaction wave. In particular, it is shown that there exists a
family of smooth solutions to the compressible Navier–Stokes equations that converges to the Riemann solution away from the
initial and shock layers at a rate in terms of the viscosity and the heat conductivity coefficients. This gives the first
mathematical justification of this limit for the Navier–Stokes equations to the Riemann solution that contains these two typical
nonlinear hyperbolic waves. 相似文献
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11.
We consider the two-dimensional motion of the coupled system of a viscous incompressible fluid and a rigid disc moving with
the fluid, in the whole plane. The fluid motion is described by the Navier–Stokes equations and the motion of the rigid body
by conservation laws of linear and angular momentum. We show that, assuming that the rigid disc is not allowed to rotate,
as the radius of the disc goes to zero, the solution of this system converges, in an appropriate sense, to the solution of
the Navier–Stokes equations describing the motion of only fluid in the whole plane. We also prove that the trajectory of the
centre of the disc, at the zero limit of its radius, coincides with a fluid particle trajectory. 相似文献
12.
In this paper, we study a free boundary problem for compressible spherically symmetric Navier–Stokes–Poisson equations with
degenerate viscosity coefficients and without a solid core. Under certain assumptions that are imposed on the initial data,
we obtain the global existence and uniqueness of the weak solution and give some uniform bounds (with respect to time) of
the solution. Moreover, we obtain some stabilization rate estimates of the solution. The results show that such a system is
stable under small perturbations, and could be applied to the astrophysics.
This work is supported by NSFC 10571158, Zhejiang Provincial NSF of China (Y605076) and China Postdoctoral Science Foundation
20060400335. 相似文献
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14.
Hai-Liang Li Akitaka Matsumura Guojing Zhang 《Archive for Rational Mechanics and Analysis》2010,196(2):681-713
The compressible Navier–Stokes–Poisson (NSP) system is considered in ${\mathbb {R}^3}The compressible Navier–Stokes–Poisson (NSP) system is considered in
\mathbb R3{\mathbb {R}^3} in the present paper, and the influences of the electric field of the internal electrostatic potential force governed by
the self-consistent Poisson equation on the qualitative behaviors of solutions is analyzed. It is observed that the rotating
effect of electric field affects the dispersion of fluids and reduces the time decay rate of solutions. Indeed, we show that
the density of the NSP system converges to its equilibrium state at the same L
2-rate
(1+t)-\frac 34{(1+t)^{-\frac {3}{4}}} or L
∞-rate (1 + t)−3/2 respectively as the compressible Navier–Stokes system, but the momentum of the NSP system decays at the L
2-rate
(1+t)-\frac 14{(1+t)^{-\frac {1}{4}}} or L
∞-rate (1 + t)−1 respectively, which is slower than the L
2-rate
(1+t)-\frac 34{(1+t)^{-\frac {3}{4}}} or L
∞-rate (1 + t)−3/2 for compressible Navier–Stokes system [Duan et al., in Math Models Methods Appl Sci 17:737–758, 2007; Liu and Wang, in Comm
Math Phys 196:145–173, 1998; Matsumura and Nishida, in J Math Kyoto Univ 20:67–104, 1980] and the L
∞-rate (1 + t)−p
with p ? (1, 3/2){p \in (1, 3/2)} for irrotational Euler–Poisson system [Guo, in Comm Math Phys 195:249–265, 1998]. These convergence rates are shown to be
optimal for the compressible NSP system. 相似文献
15.
Propagation of Density-Oscillations in Solutions to the Barotropic Compressible Navier–Stokes System
M. Hillairet 《Journal of Mathematical Fluid Mechanics》2007,9(3):343-376
Considering a bounded sequence of weak solutions to the compressible Navier–Stokes system, we introduce Young measures as
in [12] in order to describe a “homogenized system” satisfied in the limit. We then study the Cauchy problem associated to
this “homogenized system” when Young measures are convex combinations of Dirac measures. 相似文献
16.
James P. Kelliher 《Journal of Dynamics and Differential Equations》2009,21(4):631-661
We develop the concept of an infinite-energy statistical solution to the Navier–Stokes and Euler equations in the whole plane.
We use a velocity formulation with enough generality to encompass initial velocities having bounded vorticity, which includes
the important special case of vortex patch initial data. Our approach is to use well-studied properties of statistical solutions
in a ball of radius R to construct, in the limit as R goes to infinity, an infinite-energy solution to the Navier–Stokes equations. We then construct an infinite-energy statistical
solution to the Euler equations by making a vanishing viscosity argument. 相似文献
17.
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. 相似文献
18.
Feimin Huang Jing Li Akitaka Matsumura 《Archive for Rational Mechanics and Analysis》2010,197(1):89-116
We are concerned with the large-time behavior of solutions of the Cauchy problem to the one-dimensional compressible Navier–Stokes
system for ideal polytropic fluids, where the far field states are prescribed. When the corresponding Riemann problem for
the compressible Euler system admits the solution consisting of contact discontinuity and rarefaction waves, it is proved
that for the one-dimensional compressible Navier–Stokes system, the combination wave of a “viscous contact wave”, which corresponds
to the contact discontinuity, with rarefaction waves is asymptotically stable, provided the strength of the combination wave
is suitably small. This result is proved by using elementary energy methods. 相似文献
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20.
Peter Kuku?ka 《Journal of Mathematical Fluid Mechanics》2011,13(2):173-189
This paper studies the asymptotic limit for solutions to the equations of magnetohydrodynamics, specifically, the Navier–Stokes–Fourier
system describing the evolution of a compressible, viscous, and heat conducting fluid coupled with the Maxwell equations governing
the behavior of the magnetic field, when Mach number and Alfvén number tends to zero. The introduced system is considered
on a bounded spatial domain in
\mathbbR3{\mathbb{R}^{3}}, supplemented with conservative boundary conditions. Convergence towards the incompressible system of the equations of magnetohydrodynamics
is shown. 相似文献