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1.
This paper is devoted to the study of the Cauchy problem of incompressible magneto‐hydrodynamics system in the framework of Besov spaces. In the case of spatial dimension n?3, we establish the global well‐posedness of the Cauchy problem of an incompressible magneto‐hydrodynamics system for small data and the local one for large data in the Besov space ? (?n), 1?p<∞ and 1?r?∞. Meanwhile, we also prove the weak–strong uniqueness of solutions with data in ? (?n)∩L2(?n) for n/2p+2/r>1. In the case of n=2, we establish the global well‐posedness of solutions for large initial data in homogeneous Besov space ? (?2) for 2<p<∞ and 1?r<∞. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
2.
A multilevel finite element method in space‐time for the two‐dimensional nonstationary Navier‐Stokes problem is considered. The method is a multi‐scale method in which the fully nonlinear Navier‐Stokes problem is only solved on a single coarsest space‐time mesh; subsequent approximations are generated on a succession of refined space‐time meshes by solving a linearized Navier‐Stokes problem about the solution on the previous level. The a priori estimates and error analysis are also presented for the J‐level finite element method. We demonstrate theoretically that for an appropriate choice of space and time mesh widths: hj ~ h, kj ~ k, j = 2, …, J, the J‐level finite element method in space‐time provides the same accuracy as the one‐level method in space‐time in which the fully nonlinear Navier‐Stokes problem is solved on a final finest space‐time mesh. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005 相似文献
3.
A. Kh. Khanmamedov 《Mathematical Methods in the Applied Sciences》2010,33(2):177-187
In this paper the long‐time behaviour of the solutions of 2‐D wave equation with a damping coefficient depending on the displacement is studied. It is shown that the semigroup generated by this equation possesses a global attractor in H(Ω) × L2(Ω) and H2(Ω)∩H(Ω) × H(Ω). Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
4.
Yinnian He 《Numerical Methods for Partial Differential Equations》2005,21(5):875-904
In this article we consider a spectral Galerkin method with a semi‐implicit Euler scheme for the two‐dimensional Navier‐Stokes equations with H2 or H1 initial data. The H2‐stability analysis of this spectral Galerkin method shows that for the smooth initial data the semi‐implicit Euler scheme admits a large time step. The L2‐error analysis of the spectral Galerkin method shows that for the smoother initial data the numerical solution u exhibits faster convergence on the time interval [0, 1] and retains the same convergence rate on the time interval [1, ∞). © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005. 相似文献
5.
Bollobás and Thomason showed that every 22k‐connected graph is k‐linked. Their result used a dense graph minor. In this paper, we investigate the ties between small graph minors and linkages. In particular, we show that a 6‐connected graph with a K minor is 3‐linked. Further, we show that a 7‐connected graph with a K minor is (2,5)‐linked. Finally, we show that a graph of order n and size at least 7n?29 contains a K minor. © 2005 Wiley Periodicals, Inc. J Graph Theory 49: 75–91, 2005 相似文献
6.
Qingfang Liu Yanren Hou Qingchang Liu 《Numerical Methods for Partial Differential Equations》2013,29(5):1504-1521
A two‐level method in space and time for the time‐dependent Navier‐Stokes equations is considered in this article. The approximate solution uM∈HM is decomposed into the large eddy component v∈Hm(m < M) and the small eddy component w∈H. We obtain the large eddy component v by solving a standard Galerkin equation in a coarse‐level subspace Hm with a time step length k, whereas the small eddy component w is derived by solving a linear equation in an orthogonal complement subspace H with a time step length pk, where p is a positive integer. The analysis shows that our two‐level scheme has long‐time stability and can reach the same accuracy as the standard Galerkin method in fine‐level subspace HM for an appropriate configuration of p and m. Moreover, some numerical examples are provided to complement our theoretical analysis. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013 相似文献
7.
G. Matthies P. Skrzypacz L. Tobiska 《Numerical Methods for Partial Differential Equations》2005,21(4):701-725
For the Poisson equation on rectangular and brick meshes it is well known that the piecewise linear conforming finite element solution approximates the interpolant to a higher order than the solution itself. In this article, this type of supercloseness property is established for a special interpolant of the Q2 ? P element applied to the 3D stationary Stokes and Navier‐Stokes problem, respectively. Moreover, applying a Q3 ? P postprocessing technique, we can also state a superconvergence property for the discretization error of the postprocessed discrete solution to the solution itself. Finally, we show that inhomogeneous boundary values can be approximated by the Lagrange Q2‐interpolation without influencing the superconvergence property. Numerical experiments verify the predicted convergence rates. Moreover, a cost‐benefit analysis between the two third‐order methods, the post‐processed Q2 ? P discretization, and the Q3 ? P discretization is carried out. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005 相似文献
8.
For a prime p, we give a construction of perfect nonlinear functions from ? to ? when either of the following conditions holds: (1) n≥p; (2) n<p, and n is a composite number or is the sum of positive composite numbers. It follows that when n≥12, there is a perfect nonlinear function from ? to ? for any prime p. © 2009 Wiley Periodicals, Inc. J Combin Designs 17: 229‐239, 2009 相似文献
9.
Wojciech M. Zaja̧czkowski 《Mathematical Methods in the Applied Sciences》2011,34(5):544-562
We consider an initial‐boundary value problem for nonstationary Stokes system in a bounded domain Omega??3 with slip boundary conditions. We assume that Ω is crossed by an axis L. Let us introduce the following weighted Sobolev spaces with finite norms: and where ?(x) = dist{x, L}. We proved the result. Given the external force f∈L2, ?µ(ΩT), initial velocity v0∈H(Ω), µ∈?+\? there exist velocity v∈H(ΩT) and the pressure p, ?p∈L2, ?µ(ΩT) and a constant c, independent of v, p, f, such that As we consider the Stokes system in weighted Sobolev spaces the following two things must be used:
- 1. the slip boundary condition and
- 2. the Helmholtz–Weyl decomposition.
10.
We construct cyclically resolvable (v, 4, 1) designs and cyclic triple whist tournaments TWh(v) for all v of the form 3p…p + 1, where the pi are primes ≡ 1 (mod 4), such that each P1 ? 1 is divisible by the same power of 2. © 1993 John Wiley & Sons, Inc. 相似文献
11.
Thomas Schott 《Mathematische Nachrichten》1998,196(1):231-250
This paper is a continuation of [8]. We study weighted function spaces of type B and F on the Euclidean space Rn, where u is a weight function of at most exponential growth. In particular, u(χ (±|χ|) is an admissible weight. We deal with atomic decompositions of these spaces. Furthermore, we prove that the spaces B and F are isomorphic to the corresponding unweighted spaces B and F. 相似文献
12.
We prove stability of the kink solution of the Cahn‐Hilliard equation ∂tu = ∂( ∂u − u/2 + u3/2), x ∈ ℝ. The proof is based on an inductive renormalization group method, and we obtain detailed asymptotics of the solution as t → ∞. We prove stability of the kink solution of the Cahn‐Hilliard equation ∂tu = ∂( ∂u − u/2 + u3/2), x ∈ ℝ. The proof is based on an inductive renormalization group method, and we obtain detailed asymptotics of the solution as t → ∞. © 1999 John Wiley & Sons, Inc. 相似文献
13.
This article analyzes the solution of the integrated forms of fourth‐order elliptic differential equations on a rectilinear domain using a spectral Galerkin method. The spatial approximation is based on Jacobi polynomials P (x), with α, β ∈ (?1, ∞) and n the polynomial degree. For α = β, one recovers the ultraspherical polynomials (symmetric Jacobi polynomials) and for α = β = ?½, α = β = 0, the Chebyshev of the first and second kinds and Legendre polynomials respectively; and for the nonsymmetric Jacobi polynomials, the two important special cases α = ?β = ±½ (Chebyshev polynomials of the third and fourth kinds) are also recovered. The two‐dimensional version of the approximations is obtained by tensor products of the one‐dimensional bases. The various matrix systems resulting from these discretizations are carefully investigated, especially their condition number. An algebraic preconditioning yields a condition number of O(N), N being the polynomial degree of approximation, which is an improvement with respect to the well‐known condition number O(N8) of spectral methods for biharmonic elliptic operators. The numerical complexity of the solver is proportional to Nd+1 for a d‐dimensional problem. This operational count is the best one can achieve with a spectral method. The numerical results illustrate the theory and constitute a convincing argument for the feasibility of the method. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009 相似文献
14.
In this paper we prove subelliptic estimates for operators of the form Δx + λ2 (x)S in ?N = ? × ?, where the operator S is an elliptic integro - differential operator in ?N and λ is a nonnegative Lipschitz continuous function. 相似文献
15.
Let ex2(n, K) be the maximum number of edges in a 2‐colorable K‐free 3‐graph (where K={123, 124, 134} ). The 2‐chromatic Turán density of K is $\pi_{2}({K}_{4}^-) =lim_{{n}\to \infty} {ex}_{2}({n}, {K}_{4}^-)/\left(_{3}^{n}\right)Let ex2(n, K) be the maximum number of edges in a 2‐colorable K‐free 3‐graph (where K={123, 124, 134} ). The 2‐chromatic Turán density of K is $\pi_{2}({K}_{4}^-) =lim_{{n}\to \infty} {ex}_{2}({n}, {K}_{4}^-)/\left(_{3}^{n}\right)$. We improve the previously best known lower and upper bounds of 0.25682 and 3/10?ε, respectively, by showing that This implies the following new upper bound for the Turán density of K In order to establish these results we use a combination of the properties of computer‐generated extremal 3‐graphs for small n and an argument based on “super‐saturation”. Our computer results determine the exact values of ex(n, K) for n≤19 and ex2(n, K) for n≤17, as well as the sets of extremal 3‐graphs for those n. © 2009 Wiley Periodicals, Inc. J Combin Designs 18: 105–114, 2010 相似文献
16.
Charanjit S. Jutla Anindya C. Patthak Atri Rudra David Zuckerman 《Random Structures and Algorithms》2009,35(2):163-193
We present an efficient randomized algorithm to test if a given function f : ?? → ??p (where p is a prime) is a low‐degree polynomial. This gives a local test for Generalized Reed‐Muller codes over prime fields. For a given integer t and a given real ε > 0, the algorithm queries f at O( ) points to determine whether f can be described by a polynomial of degree at most t. If f is indeed a polynomial of degree at most t, our algorithm always accepts, and if f has a relative distance at least ε from every degree t polynomial, then our algorithm rejects f with probability at least . Our result is almost optimal since any such algorithm must query f on at least points. © 2009 Wiley Periodicals, Inc. Random Struct. Alg., 2009 相似文献
17.
Paweł Konieczny 《Mathematical Methods in the Applied Sciences》2009,32(15):1929-1963
We construct Lp‐estimates for the inhomogeneous Oseen system studied in a two‐dimensional exterior domain Ω with inhomogeneous slip boundary conditions. The kernel of the paper is a result for the half space ?. Analysis of this model system shows us a parabolic character of the studied problem, resulting as an appearance of the wake region behind the obstacle. Main tools are given by the Fourier analysis to obtain the maximal regularity estimates. The results imply the solvability for the Navier–Stokes system for small velocity at infinity. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
18.
Yinnian He Kaitai Li Chunshan Zhao 《Numerical Methods for Partial Differential Equations》2004,20(5):723-741
This article provides a stability analysis for the backward Euler schemes of time discretization applied to the spatially discrete spectral standard and nonlinear Galerkin approximations of the nonstationary Navier‐Stokes equations with some appropriate assumption of the data (λ, u0, f). If the backward Euler scheme with the semi‐implicit nonlinear terms is used, the spectral standard and nonlinear Galerkin methods are uniform stable under the time step constraint Δt ≤ (2/λλ1). Moreover, if the backward Euler scheme with the explicit nonlinear terms is used, the spectral standard and nonlinear Galerkin methods are uniform stable under the time step constraints Δt = O(λ) and Δt = O(λ), respectively, where λ ≤ λ, which shows that the restriction on the time step of the spectral nonlinear Galerkin method is less than that of the spectral standard Galerkin method. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2004 相似文献
19.
We consider a domain Ω in ?n of the form Ω = ?l × Ω′ with bounded Ω′ ? ?n?l. In Ω we study the Dirichlet initial and boundary value problem for the equation ? u + [(? ? ?… ? ?)m + (? ? ?… ? ?)m]u = fe?iωt. We show that resonances can occur if 2m ≥ l. In particular, the amplitude of u may increase like tα (α rational, 0<α<1) or like in t as t∞∞. Furthermore, we prove that the limiting amplitude principle holds in the remaining cases. 相似文献
20.
Stefano Fanelli 《Journal of Graph Theory》1980,4(4):371-375
Let d1 d2 dp denote the nonincreasing sequence d1, …, d1, d2, …, d2, …, dp, …, dp, where the term di appears ki times (i = 1, 2, …, p). In this work the author proves that the maximal 2-sequences: 7361515, 7561517, 7761519 are planar graphical, in contrast to a conjecture by Schmeichel and Hakimi. 相似文献