共查询到20条相似文献,搜索用时 31 毫秒
1.
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
2.
We show the existence of time periodic solutions of the Navier–Stokes equations in bounded domains of
\mathbb R3{\mathbb R^3} with inhomogeneous boundary conditions in the strong and weak sense. In particular, for weak solutions, we deal with more
generalized conditions on the boundary data for Leray’s problem. 相似文献
3.
Yasushi Taniuchi 《Mathematische Zeitschrift》2009,261(3):597-615
We present a uniqueness theorem for time-periodic solutions to the Navier–Stokes equations in unbounded domains. Thus far,
results on the uniqueness of time-periodic solutions to the Navier–Stokes equations in unbounded domain, roughly speaking,
have only found that a small time-periodic L
n
-solution is unique within the class of solutions which have sufficiently small L
∞(L
n
)-norm. In this paper, we show that a small time-periodic L
n
-solution is unique within the class of all time-periodic L
n
-solutions, which contains large solutions. We also consider the uniqueness of solutions in weak-L
n
space. The proof of the present uniqueness theorem is based on the method of dual equations.
相似文献
4.
By using the linear independent fundamental solutions of the linear variational equation
along the heteroclinic loop to establish a suitable local coordinate system in some small tubular neighborhood
of the heteroclinic loop, the Poincaré map is constructed to study the bifurcation problems of
a fine 3–point loop in higher dimensional space. Under some transversal conditions and the non–twisted
condition, the existence, coexistence and incoexistence of 2–point–loop, 1–homoclinic orbit, simple 1–periodic orbit and 2–fold
1–periodic orbit, and the number of 1–periodic orbits are studied. Moreover,
the bifurcation surfaces and existence regions are given. Lastly, the above bifurcation results are applied
to a planar system and an inside stability criterion is obtained.
This work is supported by the National Natural Science Foundation of China (10371040), the Shanghai Priority
Academic Disciplines and the Scientific Research Foundation of Linyi Teacher’s University 相似文献
5.
Maurizio Badii 《Annali dell'Universita di Ferrara》2008,54(1):1-10
This paper deals with the existence of weak periodic solutions for a model describing the electrical heating of a conductor
taking into account the Joule–Thomson effect. The periodicity of solutions is established utilizing the classical Lax–Milgram
theorem and the Schauder fixed point theorem.
相似文献
6.
Luigi Manca 《Applied Mathematics and Optimization》2008,57(3):329-348
The dynamic programming approach for the control of a 3D flow governed by the stochastic Navier–Stokes equations for incompressible fluid in a bounded domain is studied. By a compactness
argument, existence of solutions for the associated Hamilton–Jacobi–Bellman equation is proved. Finally, existence of an optimal
control through the feedback formula and of an optimal state is discussed.
This paper has been written at Scuola Normale Superiore di Pisa and at école Normale Supérieure de Cachan, Antenne de Bretagne. 相似文献
7.
Lukáš Poul 《Central European Journal of Mathematics》2008,6(3):422-438
We consider the full Navier-Stokes-Fourier system of equations on an unbounded domain with prescribed nonvanishing boundary
conditions for the density and temperature at infinity. The topic of this article continues author’s previous works on existence
of the Navier-Stokes-Fourier system on nonsmooth domains. The procedure deeply relies on the techniques developed by Feireisl
and others in the series of works on compressible, viscous and heat conducting fluids. 相似文献
8.
Mykola M. Bokalo 《Journal of Mathematical Sciences》2011,178(1):41-64
The existence and the uniqueness of generalized solutions of a problem without initial conditions are established for linear
and nonlinear anisotropic elliptic-parabolic second-order equations in domains unbounded in spatial variables. We put the
restrictions on the behavior of solutions of the problem and the growth of its initial data at infinity. The equations have
the nonlinearity exponents depending on points of the domain of definition and the direction of differentiation. Their weak
solutions are taken from generalized Lebesgue–Sobolev spaces. 相似文献
9.
The Liouville property of a complete Riemannian manifold M (i.e., the question whether there exist non-trivial bounded harmonic functions on M) attracted a lot of attention. For Cartan–Hadamard manifolds the role of lower curvature bounds is still an open problem.
We discuss examples of Cartan–Hadamard manifolds of unbounded curvature where the limiting angle of Brownian motion degenerates
to a single point on the sphere at infinity, but where nevertheless the space of bounded harmonic functions is as rich as
in the non-degenerate case. To see the full boundary the point at infinity has to be blown up in a non-trivial way. Such examples
indicate that the situation concerning the famous conjecture of Greene and Wu about existence of non-trivial bounded harmonic
functions on Cartan–Hadamard manifolds is much more complicated than one might have expected.
相似文献
10.
Blanca Climent-Ezquerra Francisco Guillén-González Marko Rojas-Medar 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2006,57(6):984-998
In this paper we prove existence of weak solution with the reproductivity in time property, for a penalized PDE’s system related
to a nematic liquid crystal model.
This problem is relatively explict when time-independent Dirichlet boundary conditions are imposed for the orientation of
crystal molecules. Nevertheless, for the time-dependent case, the treatment of the problem is completely different. The verification
of a maximum principle for weak reproductive solutions is fundamental in the argument.
Finally, the relation between reproductive and periodic in time (regular) solutions will be pointed out, differenting the
2D and 3D cases. Basically, in two-dimensional domains every reproductive solution is regular and time periodic, whereas the problem
remains open for three-dimensional domains. 相似文献
11.
On the Unique Continuation Properties for Elliptic Operators with Singular Potentials 总被引:1,自引:0,他引:1
Xiang Xing TAO Song Yan ZHANG 《数学学报(英文版)》2007,23(2):297-308
Let u be a solution to a second order elliptic equation with singular potentials belonging to Kato-Fefferman-Phong's class in Lipschitz domains. An elementary proof of the doubling property for u^2 over balls is presented, if the balls are contained in the domain or centered at some points near an open subset of the boundary on which the solution u vanishes continuously. Moreover, we prove the inner unique continuation theorems and the boundary unique continuation theorems for the elliptic equations, and we derive the Bp weight properties for the solution u near the boundary. 相似文献
12.
We consider the full system of compressible Navier–Stokes equations for heat conducting fluid. We show that the temperature
is uniformly positive for t ≥ t
0 (for any t
0 > 0) for any solutions with finite initial entropy. The assumptions on the viscosity and conductivity coefficients are minimal
(for instance, the solutions constructed by Feireisl in (Oxford Lecture Series in Mathematics and its Applications, vol 26,
2004) verify all the requirements).
相似文献
13.
On the Equivalence and Generalized of Weyl Theorem Weyl Theorem 总被引:3,自引:0,他引:3
M. BERKANI 《数学学报(英文版)》2007,23(1):103-110
We know that an operator T acting on a Banach space satisfying generalized Weyl's theorem also satisfies Weyl's theorem. Conversely we show that if all isolated eigenvalues of T are poles of its resolvent and if T satisfies Weyl's theorem, then it also satisfies generalized Weyl's theorem. We give also a sinlilar result for the equivalence of a-Weyl's theorem and generalized a-Weyl's theorem. Using these results, we study the case of polaroid operators, and in particular paranormal operators. 相似文献
14.
P. Malits 《Acta Appl Math》2007,98(2):135-152
This paper deals with a new class of Fredholm integral equations of the first kind associated with Hankel transforms of integer
order. Analysis of the equations is based on operators transforming Bessel functions of the first kind into kernels of Weber–Orr
integral transforms. Their inverse operators are established by means of new inversion theorems for the Hankel and Weber–Orr
integral transforms of functions belonging to L
1 and L
2. These operators together with the proven Paley–Wiener’s theorem for the Weber–Orr transform enable to regularize the equations
and, in special cases, to derive explicit solutions. The integral equations analyzed in this paper can be employed instead
of dual integral equations usually treated with the Cooke–Lebedev method. An example manifests that it may be preferable because
of the possibility to control norms of operators in the regularized equations.
相似文献
15.
Zhong Tan Rongcong Guo 《NoDEA : Nonlinear Differential Equations and Applications》2011,18(4):459-481
In this paper, we construct the global weak solutions to the initial-boundary problem for the Navier–Stokes system with capillarity
in the half space
\mathbbR+1{\mathbb{R}_+^1}. The result extends Eugene Tsyganov’s existence theorem which considered the problem in the finite region published in J.
Differential Equaions 245:3936–3955, 2008. 相似文献
16.
On partial regularity of suitable weak solutions to the Navier–Stokes equations in unbounded domains
Tomoyuki Suzuki 《manuscripta mathematica》2008,125(4):471-493
Consider the nonstationary Navier–Stokes equations in Ω × (0, T), where Ω is a general unbounded domain with non-compact boundary in R
3. We prove the regularity of suitable weak solutions for large |x|. It should be noted that our result also holds near the boundary. Our result extends the previous ones by Caffarelli–Kohn–Nirenberg
in R
3 and Sohr-von Wahl in exterior domains to general domains. 相似文献
17.
Existence results for periodic solutions of integro-dynamic equations on time scales 总被引:1,自引:0,他引:1
Using the topological degree method and Schaefer’s fixed point theorem, we deduce the existence of periodic solutions of nonlinear
system of integro-dynamic equations on periodic time scales. Furthermore, we provide several applications to scalar equations,
in which we develop a time scale analog of Lyapunov’s direct method and prove an analog of Sobolev’s inequality on time scales
to arrive at a priori bound on all periodic solutions. Therefore, we improve and generalize the corresponding results in Burton
et al. (Ann Mat Pura Appl 161:271–283, 1992)
相似文献
18.
Results concerning extensions of monotone operators have a long history dating back to a classical paper by Debrunner and
Flor from 1964. In 1999, Voisei obtained refinements of Debrunner and Flor’s work for n-cyclically monotone operators. His proofs rely on von Neumann’s minimax theorem as well as Kakutani’s fixed point theorem.
In this note, we provide a new proof of the central case of Voisei’s work. This proof is more elementary and rooted in convex
analysis. It utilizes only Fitzpatrick functions and Fenchel–Rockafellar duality.
相似文献
19.
An analytic technique, the homotopy analysis method (HAM), is applied to solve the generalized Benjamin–Bona–Mahony (BBM)
equation. An explicit series solution is given, different from traditional analytic techniques, our approach is independent
of knowing some parameters. This analytic method provides us with a new way to obtain series solutions of such problems. The
homotopy analysis method contains the auxiliary parameter ħ, which provides us with a simple way to adjust and control the convergence region of series solution. 相似文献
20.
A transplantation theorem for Jacobi series proved by Muckenhoupt is reinvestigated by means of a suitable variant of Calderón–Zygmund
operator theory. An essential novelty of our paper is weak type (1,1) estimate for the Jacobi transplantation operator, located
in a fairly general weighted setting. Moreover, L
p
estimates are proved for a class of weights that contains the class admitted in Muckenhoupt’s theorem.
Research of ó. Ciaurri and K. Stempak was supported by the grant MTM2006-13000-C03-03 of the DGI. Research of A. Nowak and
K. Stempak was supported by MNiSW Grant N201 054 3214285. 相似文献