共查询到20条相似文献,搜索用时 85 毫秒
1.
Jishan Fan Song Jiang Gen Nakamura Yong Zhou 《Journal of Mathematical Fluid Mechanics》2011,13(4):557-571
In this paper, logarithmically improved regularity criteria for the Navier–Stokes and the MHD equations are established in
terms of both the vorticity field and the pressure. 相似文献
2.
3.
Michael Struwe 《Journal of Mathematical Fluid Mechanics》2007,9(2):235-242
We prove a Serrin-type regularity result for Leray–Hopf solutions to the Navier–Stokes equations, extending a recent result
of Zhou [28]. 相似文献
4.
Magnus Fontes 《Journal of Mathematical Fluid Mechanics》2010,12(3):412-434
In this work we study the fully nonhomogeneous initial boundary value problem for the two-dimensional time-dependent Navier–Stokes
equations in a general open space domain in R2 with low regularity assumptions on the initial and the boundary value data. We show that the perturbed Navier–Stokes operator
is a diffeomorphism from a suitable function space onto its own dual and as a corollary we get that the Navier–Stokes equations
are uniquely solvable in these spaces and that the solution depends smoothly on all involved data. Our source data space and
solution space are in complete natural duality and in this sense, without any smallness assumptions on the data, we solve
the equations for data with optimally low regularity in both space and time. 相似文献
5.
Thomas Y. Hou Congming Li Zuoqiang Shi Shu Wang Xinwei Yu 《Archive for Rational Mechanics and Analysis》2011,199(1):117-144
We investigate the singularity formation of a nonlinear nonlocal system. This nonlocal system is a simplified one-dimensional
system of the 3D model that was recently proposed by Hou and Lei (Comm Pure Appl Math 62(4):501–564, 2009) for axisymmetric 3D incompressible Navier–Stokes equations with swirl. The main
difference between the 3D model of Hou and Lei and the reformulated 3D Navier–Stokes equations is that the convection term
is neglected in the 3D model. In the nonlocal system we consider in this paper, we replace the Riesz operator in the 3D model
by the Hilbert transform. One of the main results of this paper is that we prove rigorously the finite time singularity formation
of the nonlocal system for a large class of smooth initial data with finite energy. We also prove global regularity for a
class of smooth initial data. Numerical results will be presented to demonstrate the asymptotically self-similar blow-up of
the solution. The blowup rate of the self-similar singularity of the nonlocal system is similar to that of the 3D model. 相似文献
6.
The steady state system of isothermal Navier–Stokes equations is considered in two dimensional domain including an obstacle.
The shape optimisation problem of minimisation of the drag with respect to the admissible shape of the obstacle is defined.
The generalized solutions for the Navier–Stokes equations are introduced. The existence of an optimal shape is proved in the
class of admissible domains. In general the solutions are not unique for the problem under considerations. 相似文献
7.
We study how the number of numerically determining modes in the Navier–Stokes equations depends on the Grashof number. Consider
the two-dimensional incompressible Navier–Stokes equations in a periodic domain with a fixed time-independent forcing function.
We increase the Grashof number by rescaling the forcing and observe through numerical computation that the number of numerically
determining modes stabilizes at some finite value as the Grashof number increases. This unexpected result implies that our
theoretical understanding of continuous data assimilation is incomplete until an analytic proof which makes use of the non-linear
term in the Navier–Stokes equations is found.
相似文献
8.
New sufficient conditions of local regularity for suitable weak solutions to the non-stationary three-dimensional Navier–Stokes
equations are proved. They contain the celebrated Caffarelli–Kohn–Nirenberg theorem as a particular case.
相似文献
9.
G. Seregin 《Journal of Mathematical Fluid Mechanics》2007,9(1):34-43
A sufficient condition of regularity for solutions to the Navier–Stokes equations is proved. It generalizes the so-called
L
3,∞-case. 相似文献
10.
Chérif Amrouche M. Ángeles Rodríguez-Bellido 《Archive for Rational Mechanics and Analysis》2011,199(2):597-651
The concept of very weak solution introduced by Giga (Math Z 178:287–329, 1981) for the Stokes equations has hardly been studied in recent years for either the Navier–Stokes
equations or the Navier–Stokes type equations. We treat the stationary Stokes, Oseen and Navier–Stokes systems in the case
of a bounded open set, connected of class C1,1{\mathcal{C}^{1,1}} of
\mathbbR3{\mathbb{R}^3}. Taking up once again the duality method introduced by Lions and Magenes (Problèmes aus limites non-homogènes et applications, vols. 1 & 2, Dunod, Paris, 1968) and Giga (Math Z 178:287–329, 1981) for open sets of class C¥{\mathcal{C}^{\infty}} [see also chapter 4 of Necas (Les méthodes directes en théorie des équations elliptiques. (French) Masson et Cie, éd., Paris; Academia, éditeurs, Prague,
1967), which considers the Hilbertian case p = 2 for general elliptic operators], we give a simpler proof of the existence of a very weak solution for stationary Oseen
and Navier–Stokes equations when data are not regular enough, based on density arguments and a functional framework adequate
for defining more rigourously the traces of non-regular vector fields. In the stationary Navier–Stokes case, the results will
be valid for external forces not necessarily small, which lets us extend the uniqueness class of solutions for these equations.
Considering more regular data, regularity results in fractional Sobolev spaces will also be discussed for the three systems.
All these results can be extended to other dimensions. 相似文献
11.
Concerning to the non-stationary Navier–Stokes flow with a nonzero constant velocity at infinity, just a few results have
been obtained, while most of the results are for the flow with the zero velocity at infinity. The temporal stability of stationary
solutions for the Navier–Stokes flow with a nonzero constant velocity at infinity has been studied by Enomoto and Shibata
(J Math Fluid Mech 7:339–367, 2005), in L
p
spaces for p ≥ 3. In this article, we first extend their result to the case
\frac32 < p{\frac{3}{2} < p} by modifying the method in Bae and Jin (J Math Fluid Mech 10:423–433, 2008) that was used to obtain weighted estimates for the Navier–Stokes flow with the zero velocity at infinity. Then, by using
our generalized temporal estimates we obtain the weighted stability of stationary solutions for the Navier–Stokes flow with
a nonzero velocity at infinity. 相似文献
12.
We consider the Navier–Stokes equations in a thin domain of which the top and bottom surfaces are not flat. The velocity fields
are subject to the Navier conditions on those boundaries and the periodicity condition on the other sides of the domain. This
toy model arises from studies of climate and oceanic flows. We show that the strong solutions exist for all time provided
the initial data belong to a “large” set in the Sobolev space H
1. Furthermore we show, for both the autonomous and the nonautonomous problems, the existence of a global attractor for the
class of all strong solutions. This attractor is proved to be also the global attractor for the Leray–Hopf weak solutions
of the Navier–Stokes equations. One issue that arises here is a nontrivial contribution due to the boundary terms. We show
how the boundary conditions imposed on the velocity fields affect the estimates of the Stokes operator and the (nonlinear)
inertial term in the Navier–Stokes equations. This results in a new estimate of the trilinear term, which in turn permits
a short and simple proof of the existence of strong solutions for all time. 相似文献
13.
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
14.
15.
This paper is devoted to a scalar model of the Oseen equations, a linearized form of the Navier–Stokes equations. To control
the behavior of functions at infinity, the problem is set in weighted Sobolev spaces including anisotropic weights. In a first
step, some weighted Poincaré-type inequalities are obtained. In a second step, we establish existence, uniqueness and regularity
results. 相似文献
16.
In this short note we consider the 3D Navier–Stokes equations in the whole space, for an incompressible fluid. We provide
sufficient conditions for the regularity of strong solutions in terms of certain components of the velocity gradient. Based
on the recent results from Kukavica (J Math Phys 48(6):065203, 2007) we show these conditions as anisotropic regularity criteria
which partially interpolate results from Kukavica (J Math Phys 48(6):065203, 2007) and older results of similar type from
Penel and Pokorny (Appl Math 49(5):483–493, 2004). 相似文献
17.
Large Eddy Simulations Using the Subgrid-Scale Estimation Model and Truncated Navier–Stokes Dynamics
J. Andrzej Domaradzki Kuo Chieh Loh Patrick P. Yee 《Theoretical and Computational Fluid Dynamics》2002,15(6):421-450
We describe a procedure for large eddy simulations of turbulence which uses the subgrid-scale estimation model and truncated
Navier–Stokes dynamics. In the procedure the large eddy simulation equations are advanced in time with the subgrid-scale stress
tensor calculated from the parallel solution of the truncated Navier–Stokes equations on a mesh two times smaller in each
Cartesian direction than the mesh employed for a discretization of the resolved quantities. The truncated Navier–Stokes equations
are solved through a sequence of runs, each initialized using the subgrid-scale estimation model. The modeling procedure is
evaluated by comparing results of large eddy simulations for isotropic turbulence and turbulent channel flow with the corresponding
results of experiments, theory, direct numerical simulations, and other large eddy simulations. Subsequently, simplifications
of the general procedure are discussed and evaluated. In particular, it is possible to formulate the procedure entirely in
terms of the truncated Navier–Stokes equation and a periodic processing of the small-scale component of its solution.
Received 27 April 2001 and accepted 16 December 2001 相似文献
18.
This article characterizes the singularities of very weak solutions of 3D stationary Navier–Stokes equations in a punctured
ball which are sufficiently small in weak L
3. 相似文献
19.
We consider the Navier–Stokes equations in the thin 3D domain , where is a two-dimensional torus. The equation is perturbed by a non-degenerate random kick force. We establish that, firstly,
when ε ≪ 1, the equation has a unique stationary measure and, secondly, after averaging in the thin direction this measure converges
(as ε → 0) to a unique stationary measure for the Navier–Stokes equation on . Thus, the 2D Navier–Stokes equations on surfaces describe asymptotic in time, and limiting in ε, statistical properties of 3D solutions in thin 3D domains. 相似文献
20.
This work is concerned with applying the fractional calculus approach to the magnetohydrodynamic (MHD) pipe flow of a fractional
generalized Burgers’ fluid in a porous space by using modified Darcy’s relationship. The fluid is electrically conducting
in the presence of a constant applied magnetic field in the transverse direction. Exact solution for the velocity distribution
is developed with the help of Fourier transform for fractional calculus. The solutions for a Navier–Stokes, second grade,
Maxwell, Oldroyd-B and Burgers’ fluids appear as the limiting cases of the present analysis. 相似文献