共查询到20条相似文献,搜索用时 31 毫秒
1.
Antonio Russo 《Ricerche di matematica》2011,60(1):151-176
A classical result of Amick (Acta Math 161:71–130, 1988) on the nontriviality of the symmetric Leray solutions of the steady-state Navier–Stokes equations in the plane is extended
to Lipschitz domains. This results is compared with the famous Stokes paradox of linearized hydrodynamics and applied to a
mixed problem of some interest in the applications. 相似文献
2.
Hyunseok Kim 《Annali dell'Universita di Ferrara》2009,55(2):279-287
We study the stationary Navier–Stokes equations in a bounded domain Ω of R
3 with smooth connected boundary. The notion of very weak solutions has been introduced by Marušić-Paloka (Appl. Math. Optim.
41:365–375, 2000), Galdi et al. (Math. Ann. 331:41–74, 2005) and Kim (Arch. Ration. Mech. Anal. 193:117–152, 2009) to obtain
solvability results for the Navier–Stokes equations with very irregular data. In this article, we prove a complete solvability
result which unifies those in Marušić-Paloka (Appl. Math. Optim. 41:365–375, 2000), Galdi et al. (Math. Ann. 331:41–74, 2005)
and Kim (Arch. Ration. Mech. Anal. 193:117–152, 2009) by adapting the arguments in Choe and Kim (Preprint) and Kim and Kozono
(Preprint). 相似文献
3.
The purpose of this work is to solve the exterior Stokes problem in the half-space . We study the existence and the uniqueness of generalized solutions in weighted L
p
theory with 1 < p < ∞. Moreover, we consider the case of strong solutions and very weak solutions. This paper extends the studies done in Alliot,
Amrouche (Math. Methods Appl. 23:575–600, 2000) for an exterior Stokes problem in the whole space and in Amrouche, Bonzom
(Exterior Problems in the Half-space, submitted) for the Laplace equation in the same geometry as here.
相似文献
4.
Stochastic 2-D Navier—Stokes Equation 总被引:1,自引:0,他引:1
Abstract. In this paper we prove the existence and uniqueness of strong solutions for the stochastic Navier—Stokes equation in bounded
and unbounded domains. These solutions are stochastic analogs of the classical Lions—Prodi solutions to the deterministic
Navier—Stokes equation. Local monotonicity of the nonlinearity is exploited to obtain the solutions in a given probability
space and this significantly improves the earlier techniques for obtaining strong solutions, which depended on pathwise solutions
to the Navier—Stokes martingale problem where the probability space is also obtained as a part of the solution. 相似文献
5.
Solution of the spectral problem for the curl and Stokes operators with periodic boundary conditions
R. S. Saks 《Journal of Mathematical Sciences》2006,136(2):3794-3811
In this paper, we establish relations between eigenvalues and eigenfunctions of the curl operator and Stokes operator (with
periodic boundary conditions). These relations show that the curl operator is the square root of the Stokes operator with
ν = 1. The multiplicity of the zero eigenvalue of the curl operator is infinite. The space L
2(Q, 2π) is decomposed into a direct sum of eigenspaces of the operator curl. For any complex number λ, the equation rot
u + λu = f and the Stokes equation −ν(Δv + λ 2v) + ∇p = f, div v = 0, are solved. Bibliography: 15 titles.
Dedicated to the memory of Olga Aleksandrovna Ladyzhenskaya
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 318, 2004, pp. 246–276. 相似文献
6.
In this paper, we study the existence and regularity of solutions to the Stokes and Oseen equations with nonhomogeneous Dirichlet boundary conditions with low regularity. We consider boundary conditions for which the normal component is not equal to zero. We rewrite the Stokes and the Oseen equations in the form of a system of two equations. The first one is an evolution equation satisfied by Pu, the projection of the solution on the Stokes space – the space of divergence free vector fields with a normal trace equal to zero – and the second one is a quasi-stationary elliptic equation satisfied by (I−P)u, the projection of the solution on the orthogonal complement of the Stokes space. We establish optimal regularity results for Pu and (I−P)u. We also study the existence of weak solutions to the three-dimensional instationary Navier–Stokes equations for more regular data, but without any smallness assumption on the initial and boundary conditions. 相似文献
7.
In this paper, we prove that any weak solution to the non-stationary Stokes system in 3D with right hand side -div f satisfying (1.4) below, belongs to C( ]0, T[; C
α (Ω)). The proof is based on Campanato-type inequalities and the existence of a local pressure introduced in Wolf [13].
Proc. Conference “Variational analysis and PDE’s”. Intern. Centre “E. Majorana”, Erice, July 5–14, 2006. 相似文献
8.
We investigate the Markov property and the continuity with respect to the initial conditions (strong Feller property) for
the solutions to the Navier–Stokes equations forced by an additive noise. First, we prove, by means of an abstract selection
principle, that there are Markov solutions to the Navier–Stokes equations. Due to the lack of continuity of solutions in the
space of finite energy, the Markov property holds almost everywhere in time. Then, depending on the regularity of the noise,
we prove that any Markov solution has the strong Feller property for regular initial conditions. We give also a few consequences
of these facts, together with a new sufficient condition for well-posedness.
相似文献
9.
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
10.
We consider the zero-velocity stationary problem of the Navier–Stokes equations of compressible isentropic flow describing
the distribution of the density ϱ of a fluid in a spatial domain Ω⊂ℝ
N
driven by a time-independent potential external force b=∇F. A sharp condition in terms of F is given for the problem to possess a unique nonnegative solution ϱ having a prescribed mass m > 0.
Received: 20 October 1997 相似文献
11.
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
12.
In this work, we study a general class of partial neutral functional differential equations. We assume that the linear part
generates an analytic semigroup and the nonlinear part is Lipschitz continuous with respect to the é-norm associated to the
linear part. We discuss the existence, uniqueness, regularity and stability of solutions. Our results are illustrated by an
example. This work extends previous results on partial functional differential equations (Fitzgibbon and Parrot, Nonlinear
Anal., TMA 16, 479–487 (1991), Hale, Rev. Roum. Math. Pures Appl. 39, 339–344 (1994), Hale, Resen. Inst. Mat. Estat. Univ. Sao Paulo 1, 441–457 (1994), Travis and Webb, Trans. Am. Math. Soc. 240 129–143 (1978), Wu and Xia, J. Differ. Equ. 124 247–278 (1996)).
Mathematics Subject Classification (1991) 34K20, 34K30, 34K40, 47D06 相似文献
13.
We study some connections between Liouville type theorems and local properties of nonnegative solutions to conformal k-hessian equations by making use of an elementary lemma for all positive functions in Li and Zhang (J. Anal. Math. 90 (2003), 27–87) and related Liouville type theorems in Li and Li (Acta. Math. 195 (2005), 117–154).
Research of the second author is supported by Tianyuan Fund of Mathematics (10826061). 相似文献
14.
We present various versions of generalized Aleksandrov–Bakelman–Pucci (ABP) maximum principle for L
p
-viscosity solutions of fully nonlinear second-order elliptic and parabolic equations with possibly superlinear-growth gradient
terms and unbounded coefficients. We derive the results via the “iterated” comparison function method, which was introduced
in our previous paper (Koike and Święch in Nonlin. Diff. Eq. Appl. 11, 491–509, 2004) for fully nonlinear elliptic equations. Our results extend those of (Koike and Święch in Nonlin. Diff. Eq.
Appl. 11, 491–509, 2004) and (Fok in Comm. Partial Diff. Eq. 23(5–6), 967–983) in the elliptic case, and of (Crandall et al. in Indiana Univ. Math. J. 47(4), 1293–1326, 1998; Comm. Partial Diff. Eq. 25, 1997–2053, 2000; Wang in Comm. Pure Appl. Math. 45, 27–76, 1992) and (Crandall and Święch in Lecture Notes in Pure and Applied Mathematics, vol. 234. Dekker, New York, 2003)
in the parabolic case.
Dedicated to Hitoshi Ishii on the occasion of his 60th birthday. 相似文献
15.
Vsevolod A. Solonnikov 《Annali dell'Universita di Ferrara》2006,52(1):137-172
Abstract We prove the solvability of the evolution Stokes problem in bounded or exterior domain Ω∈ Rn under the assumption that the initial value of the velocity vector field v0 belongs to Cs(Ω),
(in particular, it can be only continuous). The solution is obtained in some weighted H?lder spaces. This result makes it
possible to prove the local solvability of a nonlinear problem under the same assumption concerning v0.
Keywords: Stokes equations, Weighted norms
Mathematics Subject Classification (2000): 35Q30, 76D03 相似文献
16.
Xiao-jing Cai Quan-sen Jiu Chun-yan Xue 《应用数学学报(英文版)》2007,23(4):637-650
In this paper,the Dirichlet problem of Stokes approximate of non-homogeneous incompressibleNavier-Stokes equations is studied.It is shown that there exist global weak solutions as well as global andunique strong solution for this problem,under the assumption that initial density ρ_0(x)is bounded away from0 and other appropriate assumptions(see Theorem 1 and Theorem 2).The semi-Galerkin method is applied toconstruct the approximate solutions and a prior estimates are made to elaborate upon the compactness of theapproximate solutions. 相似文献
17.
Futoshi Takahashi 《Calculus of Variations and Partial Differential Equations》2007,29(4):509-520
We continue to study the asymptotic behavior of least energy solutions to the following fourth order elliptic problem (E
p
): as p gets large, where Ω is a smooth bounded domain in R
4
. In our earlier paper (Takahashi in Osaka J. Math., 2006), we have shown that the least energy solutions remain bounded uniformly
in p and they have one or two “peaks” away form the boundary. In this note, following the arguments in Adimurthi and Grossi (Proc.
AMS 132(4):1013–1019, 2003) and Lin and Wei (Comm. Pure Appl. Math. 56:784–809, 2003), we will obtain more sharper estimates
of the upper bound of the least energy solutions and prove that the least energy solutions must develop single-point spiky
pattern, under the assumption that the domain is convex. 相似文献
18.
Mathias Schulze 《manuscripta mathematica》2007,123(4):373-379
From the degree zero part of the logarithmic vector fields along analgebraic hypersurface singularity we identify the maximal
multihomogeneity of a defining equation in form of a maximal algebraic torus in the embedded automorphism group. We show that
all such maximal tori are conjugate and in one–to–one correspondence to maximal tori in the linear jet of the embedded automorphism
group. These results are motivated by Kyoji Saito’s characterization of quasihomogeneity for isolated hypersurface singularities
[Saito in Invent. Math. 14, 123–142 (1971)] and extend previous work with Granger and Schulze [Compos. Math. 142(3), 765–778 (2006), Theorem 5.4] and of Hauser and Müller [Nagoya Math. J. 113, 181–186 (1989), Theorem 4]. 相似文献
19.
Agarwal and Bressoud (Pacific J. Math.
136(2) (1989) 209–228) defined a class of weighted lattice paths and interpreted several q-series combinatorially. Using the same class of lattice paths, Agarwal (Utilitas Math.
53 (1998) 71–80; ARS Combinatoria
76 (2005) 151–160) provided combinatorial interpretations for several more q-series. In this paper, a new class of weighted lattice paths, which we call associated lattice paths is introduced. It is
shown that these new lattice paths can also be used for giving combinatorial meaning to certain q-series. However, the main advantage of our associated lattice paths is that they provide a graphical representation for partitions
with n + t copies of n introduced and studied by Agarwal (Partitions with n copies of n, Lecture Notes in Math., No. 1234 (Berlin/New York: Springer-Verlag) (1985) 1–4) and Agarwal and Andrews (J. Combin. Theory
A45(1) (1987) 40–49). 相似文献
20.
Izabela Malinowska 《Archiv der Mathematik》2009,93(2):99-109
In this paper we find the structure for the automorphism group of a split metacyclic 2-group G. It can be seen as a continuation of the paper (Curran in Arch. Math. 89 (2007), 10–23) and it makes it complete. We propose a different approach to the problem than in the paper (Curran in Arch.
Math. 89 (2007), 10–23). Our intention is to show that apart from some cases of 2-groups AutG has a structure similar to that of a direct product of two groups with no common direct factor [which was considered in Bidwell,
Curran, and McCaughan (Arch. Math. 86 (2006), 481–489)].
相似文献