共查询到20条相似文献,搜索用时 15 毫秒
1.
研究了可压缩Navier-Stokes方程组
球对称弱解的大时间行为. 假设压强
$p(\varrho)=\varrho^\gamma$, 绝热指数$\gamma>1$, 外力是球对称的. 证明了假如外力满足一定的正则性及某种结构性条件, 则当时间
趋于无穷大时, 密度将趋于其对应的静止问题的唯一解. 相似文献
2.
A stationary velocity field of the flow of a gaseous medium generated by uniform radial injection from the surface of a spherical particle near a wall is considered in the Stokes' approximation. Bispherical coordinates are used to write the expression for the stream function. A formula is obtained for the force acting on the spherical particle when there is an arbitrary mass flow from its surface, generalizing earlier results /1, 2/. An expression for the force acting on the particle is obtained for the case of spherically symmetric injection from the surface of the particle, and asymptotic formulas at short and long distances from the wall are studied.
An analogous problem concerning the forces of interaction between two spherical particles of the same radius, when uniform injection of equal intensity takes place from their surfaces, is discussed. This is equivalent to the problem of the interaction of a spherical particle with a free surface. A general expression for the force of interaction, and its asymptotic forms for short and long distances, are obtained. 相似文献
3.
L. D. Eskin 《Russian Mathematics (Iz VUZ)》2008,52(8):48-57
We consider the Cauchy problem for the Boussinesq equation which describes filtration of a gas in a spherically symmetric porous medium. For the self-similar solution to this problem we construct a formal in the neighborhood of the point r → ∞ expansion and a convergent near r = 0 one. 相似文献
4.
Landweber iterative method for an inverse source problem of time-fractional diffusion-wave equation on spherically symmetric domain 下载免费PDF全文
In this paper, an inverse source problem of time-fractional diffusion-wave equation on spherically symmetric domain is considered. In general, this problem is ill-posed. Landweber iterative method is used to solve this inverse source problem. The error estimates between the regularization solution and the exact solution are derived by an a-priori and an a-posteriori regularization parameters choice rules. The numerical examples are presented to verify the efficiency and accuracy of the proposed methods. 相似文献
5.
We study the initial boundary value problem to the system of the compressible Navier-Stokes equations coupled with the Maxwell equations through the Lorentz force in a bounded annulus Ω of R3. And a result on the existence and uniqueness of global spherically symmetric classical solutions is obtained. Here the initial data could be large and initial vacuum is allowed. 相似文献
6.
Lan Zhang 《Mathematical Methods in the Applied Sciences》2019,42(8):2785-2824
In this article, we are concerned with the asymptotic behavior of spherically symmetric solution of a viscous radiative and reactive gas in a field of external force in an unbounded domain exterior to the unit sphere in for n ≥ 3. The global solution is proved to exist uniquely and converges to the stationary solution as time tends to infinity for large initial data. It is crucial to deduce uniform positive lower and upper bounds on the specific volume and the temperature. 相似文献
7.
The study of Lévy processes on local fields has been initiated by Albeverio et al. (1985)–(1998) and Evans (1989)–(1998). In this paper, a decomposition theorem for Lévy processes on local fields is given in terms of a structure result for measures on local fields and a Lévy–Khinchine representation. It is shown that a measure on a local field can be decomposed into three parts: a spherically symmetric measure, a totally non-spherically symmetric measure and a singular measure. We show that if the Radon–Nikodym derivative of the absolutely continuous part of a Lévy measure on a local field is locally constant, the Lévy process is the sum of a spherically symmetric random walk, a finite or countable set of totally non, spherically symmetric Lévy processes with single balls as support of their Lévy measure, end a singular Lévy process. These processes are independent. Explicit formulae for the transition function are obtained. 相似文献
8.
Motivated by the central limit problem for convex bodies, we study normal approximation of linear functionals of high-dimensional
random vectors with various types of symmetries. In particular, we obtain results for distributions which are coordinatewise
symmetric, uniform in a regular simplex, or spherically symmetric. Our proofs are based on Stein’s method of exchangeable
pairs; as far as we know, this approach has not previously been used in convex geometry. The spherically symmetric case is
treated by a variation of Stein’s method which is adapted for continuous symmetries.
This work was done while at Stanford University. 相似文献
9.
In this note, by constructing suitable approximate solutions, we prove the existence of global weak solutions to the compressible Navier–Stokes equations with density-dependent viscosity coefficients in the whole space or exterior domain, when the initial data are spherically symmetric. In particular, we prove the existence of spherically symmetric solutions to the Saint-Venant model for shallow water in the whole space (or exterior domain). 相似文献
10.
Summary. The convective dynamo is the generation of a magnetic field by the convective motion of an electrically conducting fluid.
We assume a spherical domain and spherically invariant basic equations and boundary conditions. The initial state of rest
is then spherically symmetric. A first instability leads to purely convective flows, the pattern of which is selected according
to the known classification of O(3) -symmetry-breaking bifurcation theory. A second instability can then lead to the dynamo effect. Computing this instability
is now a purely numerical problem, because the convective flow is known only by its numerical approximation. However, since
the convective flow can still possess a nontrivial symmetry group G
0
, this is again a symmetry-breaking bifurcation problem. After having determined numerically the critical linear magnetic
modes, we determine the action of G
0
in the space of these critical modes. Applying methods of equivariant bifurcation theory, we can classify the pattern selection
rules in the dynamo bifurcation. We consider various aspect ratios of the spherical fluid domain, corresponding to different
convective patterns, and we are able to describe the symmetry and generic properties of the bifurcated magnetic fields.
Received December 3, 1996; second revision received June 5, 1997; final version received January 23, 1998 相似文献
11.
Krešimir Burazin 《Journal of Optimization Theory and Applications》2018,177(2):329-344
We study the uniqueness and explicit derivation of the relaxed optimal solutions, corresponding to the minimization of weighted sum of potential energies for a mixture of two isotropic conductive materials on an annulus. Recently, it has been shown by Burazin and Vrdoljak that even for multiple-state problems, if the domain is spherically symmetric, then the proper relaxation of the problem by the homogenization method is equivalent to a simpler relaxed problem, stated only in terms of local proportions of given materials. This enabled explicit calculation of a solution on a ball, while problems on an annulus appeared to be more tedious. In this paper, we discuss the uniqueness of a solution of this simpler relaxed problem, when the domain is an annulus and we use the necessary and sufficient conditions of optimality to present a method for explicit calculation of the unique solution of this simpler proper relaxation, which is demonstrated on an example. 相似文献
12.
We solve the Laplace equation in an exterior infinite spherical domain with nonlinear (quadratic) boundary conditions on the spherical boundary. We linearize the problem and, under the additional assumption that the distinguishing function is spherically symmetric, write the solution by using the formal power series method with recursion of the series coefficients. Applying the Poincaré--Perron theorem, we describe the space of convergent formal power series and calculate its dimension. Estimating the roots of the fourth-degree characteristic polynomial corresponding to the given problem, we also calculate the dimension of the space of functions whose gradient at each point of the sphere is orthogonal to the linear combination of an axially symmetric dipole and a quadrupole. In conclusion, we state several unsolved problems arising in geophysical applications. 相似文献
13.
Weiwei Wang Fei Jiang Zhensheng Gao 《Mathematical Methods in the Applied Sciences》2012,35(9):1014-1032
In this paper, we prove the sequential stability of weak solutions over time, in relation to the Navier–Stokes system of compressible self‐gravitating fluids in a three‐dimensional domain. As a byproduct, we show that there exists at least one non‐negative solution to the stationary problem in any bounded domain with a given mass for the adiabatic constant γ > 3 ∕ 2. In particular, for the spherically symmetric case, these conclusions still hold for γ > 4 ∕ 3 or γ = 4 ∕ 3 with a small mass. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
14.
Julián Fernández Bonder Julio D. Rossi Noemi Wolanski 《Bulletin des Sciences Mathématiques》2006,130(7):565
We study the dependence on the subset A⊂Ω of the Sobolev trace constant for functions defined in a bounded domain Ω that vanish in the subset A. First we find that there exists an optimal subset that makes the trace constant smaller among all the subsets with prescribed and positive Lebesgue measure. In the case that Ω is a ball we prove that there exists an optimal hole that is spherically symmetric. In the case p=2 we prove that every optimal hole is spherically symmetric. Then, we study the behavior of the best constant when the hole is allowed to have zero Lebesgue measure. We show that this constant depends continuously on the subset and we discuss when it is equal to the Sobolev trace constant without the vanishing restriction. 相似文献
15.
A well-known open problem in general relativity, dating back to 1972, has been to prove Price’s law for an appropriate model of gravitational collapse. This law postulates inverse-power decay rates for the gravitational radiation
flux through the event horizon and null infinity with respect to appropriately normalized advanced and retarded time coordinates.
It is intimately related both to astrophysical observations of black holes and to the fate of observers who dare cross the
event horizon. In this paper, we prove a well-defined (upper bound) formulation of Price’s law for the collapse of a self-gravitating
scalar field with spherically symmetric initial data. We also allow the presence of an additional gravitationally coupled
Maxwell field. Our results are obtained by a new mathematical technique for understanding the long-time behavior of large
data solutions to the resulting coupled non-linear hyperbolic system of p.d.e.’s in 2 independent variables. The technique
is based on the interaction of the conformal geometry, the celebrated red-shift effect, and local energy conservation; we
feel it may be relevant for the problem of non-linear stability of the Kerr solution. When combined with previous work of
the first author concerning the internal structure of charged black holes, which had assumed the validity of Price’s law, our results can be applied to the strong cosmic censorship conjecture for the Einstein-Maxwell-real
scalar field system with complete spacelike asymptotically flat spherically symmetric initial data. Under Christodoulou’s
C0-formulation, the conjecture is proven to be false. 相似文献
16.
The aim of this work is to solve the inverse problem of determining an unknown source term in a spherically symmetric parabolic equation. The problem is ill-posed: the solution (if it exists) does not depend continuously on the final data. A spectral method is applied to formulate a regularized solution, and a Hölder type estimate of the error between the approximate solution and the exact solution is obtained with a suitable choice of regularization parameter. 相似文献
17.
In this paper,we study spherically symmetric Finsler metrics.By analysing the solution of the spherically symmetric dually flat equation,we construct several new families of dually flat spherically symmetric Finsler metrics. 相似文献
18.
In this paper, we prove the global existence of weak solutions to the full compressible Navier-Stokes equations in the domain exterior to a ball in R n (n=2,3) and with spherically symmetric data. 相似文献
19.
J. L. Synge 《Annali di Matematica Pura ed Applicata》1974,98(1):239-255
Summary Spherically symmetric universes are defined, and spherically symmetric solutions of Einstein's field equations in vacuo are
explored in terms of suitable coordinates. The Kruskal metric is thus obtained in a systematic way, with possibilities of
generalisation.
In honour of Professor BeniaminoSegre.
Entrata in Redazione il 16 marzo 1973. 相似文献
20.
In this article, we consider the free boundary value problem of 3D isentropic compressible Navier-Stokes equations. A blow-up criterion in terms of the maximum norm of gradients of velocity is obtained for the spherically symmetric strong solution in terms of the regularity estimates near the symmetric center and the free boundary respectively. 相似文献