共查询到20条相似文献,搜索用时 9 毫秒
1.
Ting Zhang 《Communications in Mathematical Physics》2009,287(1):211-224
In this paper, we consider a global wellposed problem for the 3-D incompressible anisotropic Navier-Stokes equations (ANS). We prove the global wellposedness for ANS provided the initial horizontal data are sufficient small in the scaling invariant Besov-Sobolev type space . In particular, the result implies the global wellposedness of ANS with large initial vertical velocity. 相似文献
2.
3.
In this paper, we consider the global wellposedness of the 3-D incompressible anisotropic Navier-Stokes equations with initial
data in the critical Besov-Sobolev type spaces B{\mathcal{B}} and
B-\frac12,\frac124{\mathcal{B}^{-\frac12,\frac12}_4} (see Definitions 1.1 and 1.2 below). In particular, we proved that there exists a positive constant C such that (ANS
ν
) has a unique global solution with initial data u0 = (u0h, u03){u_0 = (u_0^h, u_0^3)} which satisfies
||u0h||B exp(\fracCn4 ||u03||B4) £ c0n{\|u_0^h\|_{\mathcal{B}} \exp\bigl(\frac{C}{\nu^4} \|u_0^3\|_{\mathcal{B}}^4\bigr) \leq c_0\nu} or
||u0h||B-\frac12,\frac124 exp(\fracCn4 ||u03||B-\frac12,\frac1244) £ c0n{\|u_0^h\|_{\mathcal{B}^{-\frac12,\frac12}_{4}} \exp \bigl(\frac{C}{\nu^4} \|u_0^3\|_{\mathcal{B}^{-\frac12,\frac12}_{4}}^4\bigr)\leq c_0\nu} for some c
0 sufficiently small. To overcome the difficulty that Gronwall’s inequality can not be applied in the framework of Chemin-Lerner
type spaces, [(Lpt)\tilde](B){\widetilde{L^p_t}(\mathcal{B})}, we introduced here sort of weighted Chemin-Lerner type spaces, [(L2t, f)\tilde](B){\widetilde{L^2_{t, f}}(\mathcal{B})} for some apropriate L
1 function f(t). 相似文献
4.
In this note we obtain a sufficient condition on the regularity of the weak solutions to guarantee the conservation of helicity for the 3-D incompressible Euler equations. As a corollary we obtain a lower bound of the vorticities for a weak solution of the Euler equations. 相似文献
5.
We study the global regularity, for all time and all initial data in H 1/2, of a recently introduced decimated version of the incompressible 3D Navier-Stokes (dNS) equations. The model is based on a projection of the dynamical evolution of Navier-Stokes (NS) equations into the subspace where helicity (the L 2-scalar product of velocity and vorticity) is sign-definite. The presence of a second (beside energy) sign-definite inviscid conserved quadratic quantity, which is equivalent to the H 1/2-Sobolev norm, allows us to demonstrate global existence and uniqueness, of space-periodic solutions, together with continuity with respect to the initial conditions, for this decimated 3D model. This is achieved thanks to the establishment of two new estimates, for this 3D model, which show that the H 1/2 and the time average of the square of the H 3/2 norms of the velocity field remain finite. Such two additional bounds are known, in the spirit of the work of H. Fujita and T. Kato (Arch. Ration. Mech. Anal. 16:269–315, 1964; Rend. Semin. Mat. Univ. Padova 32:243–260, 1962), to be sufficient for showing well-posedness for the 3D NS equations. Furthermore, they are directly linked to the helicity evolution for the dNS model, and therefore with a clear physical meaning and consequences. 相似文献
6.
Dongho Chae 《Communications in Mathematical Physics》2007,269(2):557-569
In this paper we study the dynamical behaviors along the particle trajectories for some quantities of the 3D inviscid incompressible fluids. We construct evolution equations satisfied by scalar quantities composed of spectrum of the deformation tensor, the hessian of the pressure and the direction field of the vorticity, and study the dichotomy between the finite time singularity and the long time behaviors of the various scalar quantities.The work was supported partially by the KOSEF Grant no. R01-2005-000-10077-0. 相似文献
7.
首先,简单介绍了基于粘接元的无重叠区域分裂方法.这种方法利用变分原理,非常适合有限元近似.然后,着重讨论了这种区域分裂方法在求解不可压Navier-Stokes方程中的应用,具体包括等价变分公式的建立、通过算子分裂的时间离散、区域分裂情形下广义Stokes问题的共轭梯度迭代求解方法、空间的有限元离散.最后,以数值实验结果验证了这种区域分裂方法应用于不可压Navier-Stokes方程求解时的可靠性. 相似文献
8.
A Simplified Parallel Two-Level Iterative Method for Simulation of Incompressible Navier-Stokes Equations 下载免费PDF全文
Yueqiang Shang & Jin Qin 《advances in applied mathematics and mechanics.》2015,7(6):715-735
Based on two-grid discretization, a simplified parallel iterative finite element
method for the simulation of incompressible Navier-Stokes equations is developed
and analyzed. The method is based on a fixed point iteration for the equations on
a coarse grid, where a Stokes problem is solved at each iteration. Then, on overlapped
local fine grids, corrections are calculated in parallel by solving an Oseen problem in
which the fixed convection is given by the coarse grid solution. Error bounds of the
approximate solution are derived. Numerical results on examples of known analytical
solutions, lid-driven cavity flow and backward-facing step flow are also given to
demonstrate the effectiveness of the method. 相似文献
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10.
《Journal of Nonlinear Mathematical Physics》2013,20(3-4):301-311
Abstract Lie reduction of the Navier-Stokes equations to systems of partial differential equations in three and two independent variables and to ordinary differential equations is described. 相似文献
11.
In this paper, we study the finite time blow up of smooth solutions to the Compressible Navier-Stokes system when the initial data contain vacuums. We prove that any classical solutions of viscous compressible fluids without heat conduction will blow up in finite time, as long as the initial data has an isolated mass group (see Definition 2.2). The results hold regardless of either the size of the initial data or the far fields being vacuum or not. This improves the blowup results of Xin (Comm Pure Appl Math 51:229–240, 1998) by removing the crucial assumptions that the initial density has compact support and the smooth solution has finite total energy. Furthermore, the analysis here also yields that any classical solutions of viscous compressible fluids without heat conduction in bounded domains or periodic domains will blow up in finite time, if the initial data have an isolated mass group satisfying some suitable conditions. 相似文献
12.
Certain new cancellation properties in the vortex-stretching term are detected leading to new geometric criteria for preventing finite-time blow-up in the 3D Navier-Stokes equations. 相似文献
13.
Blow-up and Global Smooth Solutions for Incompressible Three-Dimensional Navier--Stokes Equations 下载免费PDF全文
We present some explicit self-similar blow-up solutions and some other solutions of the incompressible threedimensional Navier Stokes equations. These solutions indicate that in C^∞ the solution of Navier-Stokes equations does not always tend to a solution of Euler equations. 相似文献
14.
We study the partial regularity of a 3D model of the incompressible Navier-Stokes equations which was recently introduced
by the authors in [11]. This model is derived for axisymmetric flows with swirl using a set of new variables. It preserves
almost all the properties of the full 3D Euler or Navier-Stokes equations except for the convection term which is neglected
in the model. If we add the convection term back to our model, we would recover the full Navier-Stokes equations. In [11],
we presented numerical evidence which seems to support that the 3D model develops finite time singularities while the corresponding
solution of the 3D Navier-Stokes equations remains smooth. This suggests that the convection term play an essential role in
stabilizing the nonlinear vortex stretching term. In this paper, we prove that for any suitable weak solution of the 3D model
in an open set in space-time, the one-dimensional Hausdorff measure of the associated singular set is zero. The partial regularity
result of this paper is an analogue of the Caffarelli-Kohn-Nirenberg theory for the 3D Navier-Stokes equations. 相似文献
15.
This is a detailed study on certain dynamics of Navier-Stokes and Euler equations via a combination of analysis and numerics.
We focus upon two main aspects: (a) zero viscosity limit of the spectra of linear Navier-Stokes operator, (b) heteroclinics
conjecture for Euler equation, its numerical verification, Melnikov integral, and simulation and control of chaos. Due to
the difficulty of the problem for the full Navier-Stokes and Euler equations, we also propose and study two simpler models
of them. 相似文献
16.
JIAO Xiao-Yu 《理论物理通讯》2009,52(3):389-394
We investigate the symmetry reduction for the two-dimensional incompressible Navier-Stokes equation in conventional stream function form through Lie symmetry method and construct some similarity reduction solutions. Two special cases in [D.K. Ludlow, P.A. Clarkson, and A.P. Bassom, Stud. Appl. Math. 103 (1999) 183] and a theorem in [S.Y. Lou, M. Jia, X.Y. Tang, and F. Huang, Phys. Rev. E 75 (2007) 056318] are retrieved. 相似文献
17.
We investigate the symmetry reduction for the two-dimensional incompressible Navier Stokes equation in conventional stream function form through Lie symmetry method and construct some similarity reduction solutions. Two special cases in [D.K. Ludlow, P.A. Clarkson, and A.P. Bassom, Stud. Appl. Math. 103 (1999) 183] and a theorem in [S.Y. Lou, M. Jia, X.Y. Tang, and F. Huang, Phys. Rev. E 75 (2007) 056318] are retrieved. 相似文献
18.
The planar Navier-Stokes equation exhibits, in absence of external forces, a trivial asymptotics in time. Nevertheless the
appearence of coherent structures suggests non-trivial intermediate asymptotics which should be explained in terms of the
equation itself. Motivated by the separation of the different time scales observed in the dynamics of the Navier-Stokes equation,
we study the well-posedness and asymptotic behaviour of a constrained equation which neglects the variation of the energy
and moment of inertia. 相似文献
19.
G. Ponce R. Racke T. C. Sideris E. S. Titi 《Communications in Mathematical Physics》1994,159(2):329-341
We prove the stability of mildly decaying global strong solutions to the Navier-Stokes equations in three space dimensions. Combined with previous results on the global existence of large solutions with various symmetries, this gives the first global existence theorem for large solutions with approximately symmetric initial data. The stability of unforced 2D flow under 3D perturbations is also obtained. 相似文献
20.
In this paper, we investigate regularity conditions of the weighted type for weak solutions to the incompressible 3D MHD equations. 相似文献