共查询到20条相似文献,搜索用时 15 毫秒
1.
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
2.
Kazuyuki Tsuda 《Archive for Rational Mechanics and Analysis》2016,219(2):637-678
The existence of a time periodic solution of the compressible Navier–Stokes equation on the whole space is proved for a sufficiently small time periodic external force when the space dimension is greater than or equal to 3. The proof is based on the spectral properties of the time-T-map associated with the linearized problem around the motionless state with constant density in some weighted L ∞ and Sobolev spaces. The time periodic solution is shown to be asymptotically stable under sufficiently small initial perturbations and the L ∞ norm of the perturbation decays as time goes to infinity. 相似文献
3.
Sergey Zelik 《Journal of Mathematical Fluid Mechanics》2013,15(4):717-745
We study the so-called damped Navier–Stokes equations in the whole 2D space. The global well-posedness, dissipativity and further regularity of weak solutions of this problem in the uniformly-local spaces are verified based on the further development of the weighted energy theory for the Navier–Stokes type problems. Note that any divergent free vector field ${u_0 \in L^\infty(\mathbb{R}^2)}$ is allowed and no assumptions on the spatial decay of solutions as ${|x| \to \infty}$ are posed. In addition, applying the developed theory to the case of the classical Navier–Stokes problem in ${\mathbb{R}^2}$ , we show that the properly defined weak solution can grow at most polynomially (as a quintic polynomial) as time goes to infinity. 相似文献
4.
We study the resolvent equation associated with a linear operator L{\mathcal{L}} arising from the linearized equation for perturbations of a steady Navier–Stokes flow U*{\mathbf{U^*}}. We derive estimates which, together with a stability criterion from [33], show that the stability of U*{\mathbf{U^*}} (in the L2-norm) depends only on the position of the eigenvalues of L{\mathcal{L}}, regardless the presence of the essential spectrum. 相似文献
5.
The Vlasov–Poisson–Boltzmann System governs the time evolution of the distribution function for dilute charged particles in
the presence of a self-consistent electric potential force through the Poisson equation. In this paper, we are concerned with
the rate of convergence of solutions to equilibrium for this system over
\mathbb R3{\mathbb R^3}. It is shown that the electric field, which is indeed responsible for the lowest-order part in the energy space, reduces
the speed of convergence, hence the dispersion of this system over the full space is slower than that of the Boltzmann equation
without forces; the exact L
2-rate for the former is (1 + t)−1/4 while it is (1 + t)−3/4 for the latter. For the proof, in the linearized case with a given non-homogeneous source, Fourier analysis is employed to
obtain time-decay properties of the solution operator. In the nonlinear case, the combination of the linearized results and
the nonlinear energy estimates with the help of the proper Lyapunov-type inequalities leads to the optimal time-decay rate
of perturbed solutions under some conditions on initial data. 相似文献
6.
We establish a new local well-posedness result in the space of finite Borel measures for mild solutions of the parabolic–elliptic Patlak–Keller–Segel (PKS) model of chemotactic aggregation in two dimensions. Our result only requires that the initial measure satisfy the necessary assumption \({\max_{x \in \mathbb{R}^2} \mu (\{x\}) < 8 \pi}\) . This work improves the small-data results of Biler (Stud Math 114(2):181–192, 1995) and the existence results of Senba and Suzuki (J Funct Anal 191:17–51, 2002). Our work is based on that of Gallagher and Gallay (Math Ann 332:287–327, 2005), who prove the uniqueness and log-Lipschitz continuity of the solution map for the 2D Navier–Stokes equations (NSE) with measure-valued initial vorticity. We refine their techniques and present an alternative version of their proof which yields existence, uniqueness and Lipschitz continuity of the solution maps of both PKS and NSE. Many steps are more difficult for PKS than for NSE, particularly on the level of the linear estimates related to the self-similar spreading solutions. 相似文献
7.
For the Landau–Poisson system with Coulomb interaction in ${\mathbb{R}^{3}_{x}}$ R x 3 , we prove the global existence, uniqueness, and large time convergence rates to the Maxwellian equilibrium for solutions which start out sufficiently close. 相似文献
8.
9.
It is known that the three-dimensional Navier–Stokes system for an incompressible fluid in the whole space has a one parameter
family of explicit stationary solutions that are axisymmetric and homogeneous of degree −1. We show that these solutions are
asymptotically stable under any L
2-perturbation. 相似文献
10.
Fluid flows are very often governed by the dynamics of a mall number of coherent structures, i.e., fluid features which keep
their individuality during the evolution of the flow. The purpose of this paper is to study a low order simulation of the
Navier–Stokes equations on the basis of the evolution of such coherent structures. One way to extract some basis functions
which can be interpreted as coherent structures from flow simulations is by Proper Orthogonal Decomposition (POD). Then, by
means of a Galerkin projection, it is possible to find the system of ODEs which approximates the problem in the finite-dimensional
space spanned by the POD basis functions. It is found that low order modeling of relatively complex flow simulations, such
as laminar vortex shedding from an airfoil at incidence and turbulent vortex shedding from a square cylinder, provides good
qualitative results compared with reference computations. In this respect, it is shown that the accuracy of numerical schemes
based on simple Galerkin projection is insufficient and numerical stabilization is needed. To conclude, we approach the issue
of the optimal selection of the norm, namely the H
1 norm, used in POD for the compressible Navier–Stokes equations by several numerical tests.
Received 21 April 1999 and accepted 18 November 1999 相似文献
11.
We investigate the relationship between the time decay of the solutions u of the Navier–Stokes system on a bounded open subset of
and the time decay of the right-hand sides f. In suitable function spaces, we prove that u always inherits at least part of the decay of f, up to exponential, and that the decay properties of u depend only upon the amount and type (e.g., exponential, or power-like) of decay of f. This is done by first making clear what is meant by “type” and “amount” of decay and by next elaborating upon recent abstract
results pointing to the fact that, in linear and nonlinear PDEs, the decay of the solutions is often intimately related to
the Fredholmness of the differential operator.
This work was done while the second author was visiting the Bernoulli Center, EPFL, Switzerland, whose support is gratefully
acknowledged. 相似文献
12.
Boris Haspot 《Journal of Mathematical Fluid Mechanics》2016,18(2):243-291
We consider the compressible Navier–Stokes equations for viscous and barotropic fluids with density dependent viscosity. The aim is to investigate mathematical properties of solutions of the Navier–Stokes equations using solutions of the pressureless Navier–Stokes equations, that we call quasi solutions. This regime corresponds to the limit of highly compressible flows. In this paper we are interested in proving the announced result in Haspot (Proceedings of the 14th international conference on hyperbolic problems held in Padova, pp 667–674, 2014) concerning the existence of global weak solution for the quasi-solutions, we also observe that for some choice of initial data (irrotationnal) the quasi solutions verify the porous media, the heat equation or the fast diffusion equations in function of the structure of the viscosity coefficients. In particular it implies that it exists classical quasi-solutions in the sense that they are \({C^{\infty}}\) on \({(0,T)\times \mathbb{R}^{N}}\) for any \({T > 0}\). Finally we show the convergence of the global weak solution of compressible Navier–Stokes equations to the quasi solutions in the case of a vanishing pressure limit process. In particular for highly compressible equations the speed of propagation of the density is quasi finite when the viscosity corresponds to \({\mu(\rho)=\rho^{\alpha}}\) with \({\alpha > 1}\). Furthermore the density is not far from converging asymptotically in time to the Barrenblatt solution of mass the initial density \({\rho_{0}}\). 相似文献
13.
This paper mainly concerns the mathematical justification of a viscous compressible multi-fluid model linked to the Baer-Nunziato
model used by engineers, see for instance Ishii (Thermo-fluid dynamic theory of two-phase flow, Eyrolles, Paris, 1975), under a “stratification” assumption. More precisely, we show that some approximate finite-energy weak solutions of the
isentropic compressible Navier–Stokes equations converge, on a short time interval, to the strong solution of this viscous
compressible multi-fluid model, provided the initial density sequence is uniformly bounded with corresponding Young measures
which are linear convex combinations of m Dirac measures. To the authors’ knowledge, this provides, in the multidimensional in space case, a first positive answer
to an open question, see Hillairet (J Math Fluid Mech 9:343–376, 2007), with a stratification assumption. The proof is based on the weak solutions constructed by Desjardins (Commun Partial Differ Equ 22(5–6):977–1008, 1997) and on the existence and uniqueness of a local strong solution for the multi-fluid model established by Hillairet assuming initial density to be far from vacuum. In a first step, adapting the ideas from Hoff and Santos (Arch Ration Mech Anal 188:509–543, 2008), we prove that the sequence of weak solutions built by Desjardins has extra regularity linked to the divergence of the velocity without any relation assumption between λ and μ. Coupled with the uniform bound of the density property, this allows us to use appropriate defect measures and their nice
properties introduced and proved by Hillairet (Aspects interactifs de la m’ecanique des fluides, PhD Thesis, ENS Lyon, 2005) in order to prove that the Young measure associated to the weak limit is the convex combination of m Dirac measures. Finally, under a non-degeneracy assumption of this combination (“stratification” assumption), this provides
a multi-fluid system. Using a weak–strong uniqueness argument, we prove that this convex combination is the one corresponding
to the strong solution of the multi-fluid model built by Hillairet, if initial data are equal. We will briefly discuss this assumption. To complete the paper, we also present a blow-up criterion
for this multi-fluid system following (Huang et al. in Serrin type criterion for the three-dimensional viscous compressible flows, arXiv, 2010). 相似文献
14.
Peter Bella 《Journal of Mathematical Fluid Mechanics》2012,14(2):279-294
Ducomet et?al. (Discrete Contin Dyn Syst 11(1): 113?C130, 2004) showed the existence of global weak solutions to the Navier?CStokes?CPoisson system. We study the global behavior of such a solution. This is done by (1) proving uniqueness of a solution to the stationary system; (2) by showing convergence of a weak solution to the stationary solution. In (1) we consider only the case with repulsion. We prove our result in the case of a bounded domain with smooth boundary in ${\mathbb{R}^3}$ and also in the case of the whole space ${\mathbb{R}^3}$ . 相似文献
15.
The scale invariance properties of compressible Navier–Stokes and energy equations subject to density-weighted filtering are investigated. Scale or filter invariance forms of compressible moment equations require that two forms of generalized central second-order moments be defined—(1) product of two density-weighted sub-filter fluctuations and (2) product of one density-weighted and one un-weighted sub-filter fluctuation. The evolution equations for all required first and second order filtered moments are derived. These results provide the theoretical underpinning for variable-resolution calculations of reacting and compressible turbulent flows. 相似文献
16.
Vincenzo Ambrosio Hichem Hajaiej 《Journal of Dynamics and Differential Equations》2018,30(3):1119-1143
This paper is concerned with the following fractional Schrödinger equation where \(s\in (0,1),N> 2s, (-\Delta )^{s}\) is the fractional Laplacian, k is a bounded positive function, \(h\in L^{2}(\mathbb {R}^{N}), h\not \equiv 0\) is nonnegative and f is either asymptotically linear or superlinear at infinity. By using the s-harmonic extension technique and suitable variational methods, we prove the existence of at least two positive solutions for the problem under consideration, provided that \(|h|_{2}\) is sufficiently small.
相似文献
$$\begin{aligned} \left\{ \begin{array}{ll} (-\Delta )^{s} u+u= k(x)f(u)+h(x) \text{ in } \mathbb {R}^{N}\\ u\in H^{s}(\mathbb {R}^{N}), \, u>0 \text{ in } \mathbb {R}^{N}, \end{array} \right. \end{aligned}$$
17.
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
18.
Hyeong-Ohk Bae Young-Pil Choi Seung-Yeal Ha Moon-Jin Kang 《Journal of Mathematical Fluid Mechanics》2016,18(2):381-396
A coupled kinetic–fluid model describing the interactions between Cucker–Smale flocking particles and a Stokes fluid is presented. We demonstrate the global existence and uniqueness of strong solutions to this coupled system in a three-dimensional spatially periodic domain for initial data that are sufficiently regular, but not necessarily small. 相似文献
19.
We show that if a Leray–Hopf solution u of the three-dimensional Navier–Stokes equation belongs to C((0,T]; B-1¥,¥){C((0,T]; B^{-1}_{\infty,\infty})} or its jumps in the B-1¥,¥{B^{-1}_{\infty,\infty}}-norm do not exceed a constant multiple of viscosity, then u is regular for (0, T]. Our method uses frequency local estimates on the nonlinear term, and yields an extension of the classical Ladyzhenskaya–Prodi–Serrin
criterion. 相似文献
20.
Based on the mass transfer theory, a new mass transfer model of ion-exchange process on zeolite under liquid film diffusion
control is established, and the kinetic curves and the mass transfer coefficients of –K+ ion-exchange under different conditions were systemically determined using the shallow-bed experimental method. The results
showed that the –K+ ion-exchange rates and transfer coefficients are directly proportional to solution flow rate and temperature, and inversely
proportional to solution viscosity and the size of zeolite granules. It also showed that the transfer coefficient is not influenced
by the ion concentrations. For a large ranges of operational conditions including temperatures (10 − 75°C), flow rates (0.031 m s−1 −0.26 m s−1), liquid viscosities (1.002 × 10−3 N s m−2 − 4.44 × 10−3 N s m−2), and zeolite granular sizes (0.2 − 1.45 mm), the average mass transfer coefficients calculated by the model agree with the
experimental results very well. 相似文献