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1.
We analyze the spatial anisotropic profiles at infinity of steady Stokes and Navier–Stokes flows around a rotating obstacle.
It is shown that the Stokes flow is largely concentrated along the axis of rotation in the leading term and that a rotating
profile can be found in the second term. The leading term for Navier–Stokes flow will be an adequate Landau solution. The
proofs rely upon a detailed analysis of the associated fundamental solution tensor. 相似文献
2.
Abstract. In this paper we prove the existence and uniqueness of strong solutions for the stochastic Navier—Stokes equation in bounded
and unbounded domains. These solutions are stochastic analogs of the classical Lions—Prodi solutions to the deterministic
Navier—Stokes equation. Local monotonicity of the nonlinearity is exploited to obtain the solutions in a given probability
space and this significantly improves the earlier techniques for obtaining strong solutions, which depended on pathwise solutions
to the Navier—Stokes martingale problem where the probability space is also obtained as a part of the solution. 相似文献
3.
Stochastic 2-D Navier—Stokes Equation 总被引:1,自引:0,他引:1
Abstract. In this paper we prove the existence and uniqueness of strong solutions for the stochastic Navier—Stokes equation in bounded
and unbounded domains. These solutions are stochastic analogs of the classical Lions—Prodi solutions to the deterministic
Navier—Stokes equation. Local monotonicity of the nonlinearity is exploited to obtain the solutions in a given probability
space and this significantly improves the earlier techniques for obtaining strong solutions, which depended on pathwise solutions
to the Navier—Stokes martingale problem where the probability space is also obtained as a part of the solution. 相似文献
4.
The Stokes lines/curves are identified for the Mittag—Leffler function
When α is not real, it is found that the Stokes curves are spirals. Away from the Stokes lines/curves, exponentially improved uniform
asymptotic expansions are obtained. Near the Stokes lines/curves, Berry-type smooth transitions are achieved via the use of
the complementary error function. 相似文献
5.
Helmut Abels 《Journal of Evolution Equations》2002,2(4):439-457
In this article we prove the existence of bounded purely imaginary powers of the Stokes operator , which is defined on the space of solenoidal vector fields < q < , where is an infinite layer. It is a consequence of a special representation of the resolvent of the Stokes operator in terms of
the Stokes operator on , a composition of a trace and a Poisson operator – a singular Green operator – and a negligible part. 相似文献
6.
A. S. Mikhailov 《Journal of Mathematical Sciences》2011,178(3):282-291
A class of sufficient conditions for local boundary regularity of suitable weak solutions of nonstationary three-dimensional
Navier–Stokes equations is discussed. The corresponding results are stated in terms of functionals, which are invariant with
respect to the scaling of the Navier–Stokes equations. Bibliography: 27 titles. 相似文献
7.
A. Mikhailov 《Journal of Mathematical Sciences》2010,166(1):40-52
A class of sufficient conditions for the local boundary regularity of suitable weak solutions of nonstationary three-dimensional
Navier–Stokes equations is discussed. The corresponding results are stated in terms of functionals invariant with respect
to the scaling of Navier–Stokes equations. Bibliography: 26 titles. 相似文献
8.
In this paper,the fundamental solution of rotating generalized Stokes problem in R 3 is established.To obtain it,some fundamental solutions of other problems also are established,such as generalized Laplace problem,generalized Stokes problem and rotating Stokes problem. 相似文献
9.
Recently, the Navier–Stokes–Voight (NSV) model of viscoelastic incompressible fluid has been proposed as a regularization
of the 3D Navier–Stokes equations for the purpose of direct numerical simulations. In this work, we prove that the global
attractor of the 3D NSV equations, driven by an analytic forcing, consists of analytic functions. A consequence of this result
is that the spectrum of the solutions of the 3D NSV system, lying on the global attractor, have exponentially decaying tail,
despite the fact that the equations behave like a damped hyperbolic system, rather than the parabolic one. This result provides
additional evidence that the 3D NSV with the small regularization parameter enjoys similar statistical properties as the 3D
Navier–Stokes equations. Finally, we calculate a lower bound for the exponential decaying scale—the scale at which the spectrum
of the solution start to decay exponentially, and establish a similar bound for the steady state solutions of the 3D NSV and
3D Navier–Stokes equations. Our estimate coincides with the known bounds for the smallest length scale of the solutions of
the 3D Navier–Stokes equations, established earlier by Doering and Titi.
相似文献
10.
Very weak solutions to the stationary Stokes and Stokes resolvent problem in weighted function spaces 总被引:1,自引:0,他引:1
Katrin Schumacher 《Annali dell'Universita di Ferrara》2008,54(1):123-144
We investigate very weak solutions to the stationary Stokes and Stokes resolvent problem in function spaces with Muckenhoupt
weights. The notion used here is similar but even more general than the one used in Amann (Nonhomogeneous Navier–Stokes equations
with integrable low-regularity data. Int. Math. Ser., pp. 1–26. Kluwer Academic/Plenum Publishing, New York, 2002) or Galdi
et al. (Math. Ann. 331, 41–74, 2005). Consequently the class of solutions is enlarged. To describe boundary conditions we restrict ourselves to
more regular data. We introduce a Banach space that admits a restriction operator and that contains the solutions according
to such data.
相似文献
11.
Antonio Russo 《Ricerche di matematica》2011,60(1):151-176
A classical result of Amick (Acta Math 161:71–130, 1988) on the nontriviality of the symmetric Leray solutions of the steady-state Navier–Stokes equations in the plane is extended
to Lipschitz domains. This results is compared with the famous Stokes paradox of linearized hydrodynamics and applied to a
mixed problem of some interest in the applications. 相似文献
12.
In the first part of the paper, we give a satisfactory definition of the Stokes operator in Lipschitz domains in
\mathbbRn {\mathbb{R}^n} when boundary conditions of Neumann type are considered. We then proceed to establish optimal global Sobolev regularity results
for vector fields in the domains of fractional powers of this Neumann–Stokes operator. Finally, we study the existence, regularity,
and uniqueness of mild solutions of the Navier–Stokes system with Neumann boundary conditions. Bibliography: 43 titles. Illustrations:
2 figures. 相似文献
13.
We present a sufficient condition for the energy equality of Leray–Hopf’s weak solutions to the Navier–Stokes equations in
general unbounded 3-dimensional domains. 相似文献
14.
Finite element error estimates for 3D exterior incompressible flow with nonzero velocity at infinity
Paul Deuring 《Numerische Mathematik》2009,114(2):233-270
We consider a stationary incompressible Navier–Stokes flow in a 3D exterior domain, with nonzero velocity at infinity. In
order to approximate this flow, we use the stabilized P1–P1 finite element method proposed by Rebollo (Numer Math 79:283–319,
1998). Following an approach by Guirguis and Gunzburger (Model Math Anal Numer 21:445–464, 1987), we apply this method to
the Navier–Stokes system with Oseen term in a truncated exterior domain, under a pointwise boundary condition on the artificial
boundary. This leads to a discrete problem whose solution approximates the exterior flow, as is shown by error estimates. 相似文献
15.
Martin Franzke 《Annali dell'Universita di Ferrara》2000,46(1):161-173
We consider the nonstationary Navier-Stokes equations in an aperture domain Ω⊂R3 consisting of two halfspaces separated by a wall, but connected by a hole in this wall. In this special domain one has to
impose an auxiliary condition to single out a unique solution. This can be done by prescribing either the flux through the
hole or the pressure drop between the two halfspaces. We construct suitable Stokes operators for both of the auxiliary conditions
and show that they generate holomorphic semigroups. Then we prove the existence and uniqueness of solutions as well as a maximal
regularity estimate for the Stokes equations subject to one of the auxiliary conditions. For the corresponding Navier-Stokes
equations we prove existence and uniqueness of local in time solutions.
Sunto In questo lavoro consideriamo le equazioni di Navier-Stokes non stazionarie in un dominio con un’apertura, che consiste di due semispazi separati da una parete, ma collegati da un’apertura in quest’ultima. In questo dominio particolare è necessario imporre, per avere un’unica soluzione, una opportuna condizione ausiliaria. Questo può essere fatto sia assegnando il flusso attraverso l’apertura sia prescrivendo il salto di pressione tra i due semispazi. Qui costruiamo degli operatori di Stokes opportuni per ambedue i tipi di condizioni ausiliarie e mostriamo come essi generino semigruppi olomorfi. Dimostriamo, quindi, esistenza e unicità di soluzioni, assieme ad una stima di massima regolarità per le equazioni di Stokes soggette ad una delle condizioni ausiliarie. Per le corrispondenti equazioni di Navier-Stokes, dimostriamo esistenza e unicità di soluzioni locali nel tempo.相似文献
16.
In this paper, we apply the boundary integral method to the steady rotating Navier–Stokes equations in exterior domain. Introducing
some open ball which decomposes the exterior domain into a finite domain and a infinite domain, we obtain a coupled problem
by the steady rotating Navier–Stokes equations in finite domain and a boundary integral equation without using the artificial
boundary condition. For the coupled problem, we show the existence of solution in a convex set. 相似文献
17.
Solution of the spectral problem for the curl and Stokes operators with periodic boundary conditions
R. S. Saks 《Journal of Mathematical Sciences》2006,136(2):3794-3811
In this paper, we establish relations between eigenvalues and eigenfunctions of the curl operator and Stokes operator (with
periodic boundary conditions). These relations show that the curl operator is the square root of the Stokes operator with
ν = 1. The multiplicity of the zero eigenvalue of the curl operator is infinite. The space L
2(Q, 2π) is decomposed into a direct sum of eigenspaces of the operator curl. For any complex number λ, the equation rot
u + λu = f and the Stokes equation −ν(Δv + λ 2v) + ∇p = f, div v = 0, are solved. Bibliography: 15 titles.
Dedicated to the memory of Olga Aleksandrovna Ladyzhenskaya
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 318, 2004, pp. 246–276. 相似文献
18.
Peer Christian Kunstmann 《Czechoslovak Mathematical Journal》2010,60(2):297-313
We consider the Navier-Stokes equations in unbounded domains Ω ⊆ ℝ
n
of uniform C
1,1-type. We construct mild solutions for initial values in certain extrapolation spaces associated to the Stokes operator on
these domains. Here we rely on recent results due to Farwig, Kozono and Sohr, the fact that the Stokes operator has a bounded
H
∞-calculus on such domains, and use a general form of Kato’s method. We also obtain information on the corresponding pressure
term. 相似文献
19.
James P. Kelliher 《Mathematische Annalen》2009,343(3):701-726
We say that a solution of the Navier–Stokes equations converges in the vanishing viscosity limit to a solution of the Euler
equations if their velocities converge in the energy (L
2) norm uniformly in time as the viscosity ν vanishes. We show that a necessary and sufficient condition for the vanishing viscosity limit to hold in a disk is that the
space–time energy density of the solution to the Navier–Stokes equations in a boundary layer of width proportional to ν vanish with ν, and that one need only consider spatial variations whose frequencies in the radial or tangential direction lie in a band
centered around 1/ν.
The author was supported in part by NSF grant DMS-0705586 during the period of this work. 相似文献
20.
The Stokes phenomenon associated with the differential equationsW " = WZ (z2a2) and W" = w(z2 a2)(x2b2)isconsidered. As an application to the method introduced in paper I, somenumerical and analytical results concerning the Stokes constantsof these equations are presented. 相似文献