共查询到20条相似文献,搜索用时 31 毫秒
1.
We study the boundary-value problem associated with the Oseen system in the exterior of m Lipschitz domains of an euclidean point space
We show, among other things, that there are two positive constants
and α depending on the Lipschitz character of Ω such that: (i) if the boundary datum a belongs to Lq(∂Ω), with q ∈ [2,+∞), then there exists a solution (u, p), with
and u ∈ L∞(Ω) if a ∈ L∞(∂Ω), expressed by a simple layer potential plus a linear combination of regular explicit functions; as a consequence, u tends nontangentially to a almost everywhere on ∂Ω; (ii) if a ∈ W1-1/q,q(∂Ω), with
then ∇u, p ∈ Lq(Ω) and if a ∈ C0,μ(∂Ω), with μ ∈ [0, α), then
also, natural estimates holds. 相似文献
2.
This paper is devoted to a new finite element consistency analysis of Cauchy–Born approximations to atomistic models of crystalline materials in two and three space dimensions. Through this approach new “atomistic Cauchy–Born” models are introduced and analyzed. These intermediate models can be seen as first level atomistic/quasicontinuum approximations in the sense that they involve only short-range interactions. The analysis and the models developed herein are expected to be useful in the design of coupled atomistic/continuum methods in more than one dimension. Taking full advantage of the symmetries of the atomistic lattice, we show that the consistency error of the models considered both in energies and in dual W 1,p type norms is ${\mathcal{O}(\varepsilon^2)}$ , where ${\varepsilon}$ denotes the interatomic distance in the lattice. 相似文献
3.
Yoshihiro Ueda Tohru Nakamura Shuichi Kawashima 《Archive for Rational Mechanics and Analysis》2010,198(3):735-762
This paper is concerned with the asymptotic stability of degenerate stationary waves for viscous gases in the half space.
We discuss the following two cases: (1) viscous conservation laws and (2) damped wave equations with nonlinear convection.
In each case, we prove that the solution converges to the corresponding degenerate stationary wave at the rate t
−α/4 as t → ∞, provided that the initial perturbation is in the weighted space
L2a=L2(\mathbb R+; (1+x)a dx){L^2_\alpha=L^2({\mathbb R}_+;\,(1+x)^\alpha dx)} . This convergence rate t
−α/4 is weaker than the one for the non-degenerate case and requires the restriction α < α*(q), where α*(q) is the critical value depending only on the degeneracy exponent q. Such a restriction is reasonable because the corresponding linearized operator for viscous conservation laws cannot be dissipative
in L2a{L^2_\alpha} for α > α*(q) with another critical value α*(q). Our stability analysis is based on the space–time weighted energy method in which the spatial weight is chosen as a function
of the degenerate stationary wave. 相似文献
4.
Using a general approximation setting having the generic properties of finite-elements, we prove uniform boundedness and stability
estimates on the discrete Stokes operator in Sobolev spaces with fractional exponents. As an application, we construct approximations
for the time-dependent Stokes equations with a source term in L
p
(0, T; L
q
(Ω)) and prove uniform estimates on the time derivative and discrete Laplacian of the discrete velocity that are similar to
those in Sohr and von Wahl [20].
On long leave from LIMSI (CNRS-UPR 3251), BP 133, 91403, Orsay, France. 相似文献
5.
E. N. Barron R. R. Jensen C. Y. Wang 《Archive for Rational Mechanics and Analysis》2001,157(4):255-283
The Aronsson-Euler equation for the functional
on W
g
1, ∞(Ω, ℝ
m
, i.e., W
1, ∞ with boundary data g, is
This equation has been derived for smooth absolute minimizers, i.e., a function which minimizes F on every subdomain. We prove in this paper that for m=1, n≧ 1, or n=1, m≧ 1 an absolute minimizer of F exists in W
g
1, ∞(Ω, ℝ
m
and for m= 1, n≧ 1 any absolute minimizer of F must be a viscosity solution of the Aronsson-Euler equation.
Accepted November 13, 2000?Published online April 23, 2001 相似文献
6.
Maria Letizia Bertotti Sergey V. Bolotin 《Archive for Rational Mechanics and Analysis》2000,152(1):65-79
Natural Lagrangian systems (T,Π) on R
2 described by the equation are considered, where is a positive definite quadratic form in and Π(q) has a critical point at 0. It is constructively proved that there exist a C
∞ potential energy Π and two C
∞ kinetic energies T and such that the equilibrium q(t)≡ 0 is stable for the system (T,Π) and unstable for the system . Equivalently, it is established that for C
∞
natural systems the kinetic energy can influence the stability. In the analytic category this is not true.
Accepted: October 20, 1999 相似文献
7.
Hai-Liang Li Akitaka Matsumura Guojing Zhang 《Archive for Rational Mechanics and Analysis》2010,196(2):681-713
The compressible Navier–Stokes–Poisson (NSP) system is considered in ${\mathbb {R}^3}The compressible Navier–Stokes–Poisson (NSP) system is considered in
\mathbb R3{\mathbb {R}^3} in the present paper, and the influences of the electric field of the internal electrostatic potential force governed by
the self-consistent Poisson equation on the qualitative behaviors of solutions is analyzed. It is observed that the rotating
effect of electric field affects the dispersion of fluids and reduces the time decay rate of solutions. Indeed, we show that
the density of the NSP system converges to its equilibrium state at the same L
2-rate
(1+t)-\frac 34{(1+t)^{-\frac {3}{4}}} or L
∞-rate (1 + t)−3/2 respectively as the compressible Navier–Stokes system, but the momentum of the NSP system decays at the L
2-rate
(1+t)-\frac 14{(1+t)^{-\frac {1}{4}}} or L
∞-rate (1 + t)−1 respectively, which is slower than the L
2-rate
(1+t)-\frac 34{(1+t)^{-\frac {3}{4}}} or L
∞-rate (1 + t)−3/2 for compressible Navier–Stokes system [Duan et al., in Math Models Methods Appl Sci 17:737–758, 2007; Liu and Wang, in Comm
Math Phys 196:145–173, 1998; Matsumura and Nishida, in J Math Kyoto Univ 20:67–104, 1980] and the L
∞-rate (1 + t)−p
with p ? (1, 3/2){p \in (1, 3/2)} for irrotational Euler–Poisson system [Guo, in Comm Math Phys 195:249–265, 1998]. These convergence rates are shown to be
optimal for the compressible NSP system. 相似文献
8.
Hyeong-Ohk Bae 《Journal of Mathematical Fluid Mechanics》2008,10(4):503-530
We estimate the time decay rates in L
1, in the Hardy space and in L
∞ of the gradient of solutions for the Stokes equations on the half spaces. For the estimates in the Hardy space we adopt the
ideas in [7], and also use the heat kernel and the solution formula for the Stokes equations.
We also estimate the temporal-spatial asymptotic estimates in L
q
, 1 < q < ∞, for the Stokes solutions.
This work was supported by grant No. (R05-2002-000-00002-0(2002)) from the Basic Research Program of the Korea Science & Engineering
Foundation. 相似文献
9.
Matthias Geissert Matthias Hess Matthias Hieber Céline Schwarz Kyriakos Stavrakidis 《Journal of Mathematical Fluid Mechanics》2010,12(1):47-60
Introducing a new localization method involving Bogovskiĭ's operator we give a short and new proof for maximal Lp – Lq-estimates for the solution of the Stokes equation. Moreover, it is shown that, up to constants, the Stokes operator is an
R{\mathcal{R}}-sectorial operator in Lps(W)L^{p}_{\sigma}(\Omega), 1 < p < ¥1 < p < \infty, of R{\mathcal{R}}-angle 0, for bounded or exterior domains of Ω. 相似文献
10.
Maxime Hauray Pierre-Emmanuel Jabin 《Archive for Rational Mechanics and Analysis》2007,183(3):489-524
We prove the convergence in any time interval of a point-particle approximation of the Vlasov equation by particles initially
equally separated for a force in 1/|x|α, with
. We introduce discrete versions of the L
∞ norm and time averages of the force-field. The core of the proof is to show that these quantities are bounded and that consequently
the minimal distance between particles in the phase space is bounded from below. 相似文献
11.
Let be a domain. Suppose that f ∈ W1,1loc(Ω,R2) is a homeomorphism such that Df(x) vanishes almost everywhere in the zero set of Jf. We show that f-1 ∈ W1,1loc(f(Ω),R2) and that Df−1(y) vanishes almost everywhere in the zero set of Sharp conditions to quarantee that f−1 ∈ W1,q(f(Ω),R2) for some 1<q≤2 are also given. 相似文献
12.
Mike Cullen Wilfrid Gangbo Giovanni Pisante 《Archive for Rational Mechanics and Analysis》2007,185(2):341-363
We study the evolution of a system of n particles in . That system is a conservative system with a Hamiltonian of the form , where W
2 is the Wasserstein distance and μ is a discrete measure concentrated on the set . Typically, μ(0) is a discrete measure approximating an initial L
∞ density and can be chosen randomly. When d = 1, our results prove convergence of the discrete system to a variant of the semigeostrophic equations. We obtain that
the limiting densities are absolutely continuous with respect to the Lebesgue measure. When converges to a measure concentrated on a special d–dimensional set, we obtain the Vlasov–Monge–Ampère (VMA) system. When, d = 1 the VMA system coincides with the standard Vlasov–Poisson system. 相似文献
13.
In this paper, we establish analyticity of the Navier–Stokes equations with small data in critical Besov spaces . The main method is Gevrey estimates, the choice of which is motivated by the work of Foias and Temam (Contemp Math 208:151–180, 1997). We show that mild solutions are Gevrey regular, that is, the energy bound holds in , globally in time for p < ∞. We extend these results for the intricate limiting case p = ∞ in a suitably designed E ∞ space. As a consequence of analyticity, we obtain decay estimates of weak solutions in Besov spaces. Finally, we provide a regularity criterion in Besov spaces. 相似文献
14.
Michael G. Crandall 《Archive for Rational Mechanics and Analysis》2003,167(4):271-279
For 1<p<∞, the equation which characterizes minima of the functional u↦∫
U
|Du|
p
,dx subject to fixed values of u on ∂U is −Δ
p
u=0. Here −Δ
p
is the well-known ``p-Laplacian'. When p=∞ the corresponding functional is u↦|| |Du|2||
L∞(U)
. A new feature arises in that minima are no longer unique unless U is allowed to vary, leading to the idea of ``absolute minimizers'. Aronsson showed that then the appropriate equation is
−Δ∞
u=0, that is, u is ``infinity harmonic' as explained below. Jensen showed that infinity harmonic functions, understood in the viscosity
sense, are precisely the absolute minimizers. Here we advance results of Barron, Jensen and Wang concerning more general functionals
u↦||f(x,u,Du)||
L∞(U)
by giving a simplified derivation of the corresponding necessary condition under weaker hypotheses.
(Accepted September 6, 2002)
Published online April 14, 2003
Communicated by S. Muller 相似文献
15.
We study the values e
σ(f) of the best approximation of integrals of functions from the spaces L
p
(A, dμ) by integrals of rank σ. We determine the orders of the least upper bounds of these values as σ → ∞ in the case where the function ƒ is the product of two nonnegative functions one of which is fixed and the other varies
on the unit ball U
p
(A) of the space L
p
(A, dμ). We consider applications of the obtained results to approximation problems in the spaces S
p
ϕ.
__________
Translated from Neliniini Kolyvannya, Vol. 10, No. 4, pp. 528–559, October–December, 2007. 相似文献
16.
In this paper we derive global W
1,∞ and piecewise C
1,α estimates for solutions to divergence form elliptic equations with piecewise H?lder continuous coefficients. The novelty
of these estimates is that, even though they depend on the shape and on the size of the surfaces of discontinuity of the coefficients,
they are independent of the distance between these surfaces.
Accepted: June 8, 1999 相似文献
17.
Although the formulation of the nonlinear theory of H
∞ control has been well developed, solving the Hamilton–Jacobi–Isaacs equation remains a challenge and is the major bottleneck
for practical application of the theory. Several numerical methods have been proposed for its solution. In this paper, results
on convergence and stability for a successive Galerkin approximation approach for nonlinear H
∞ control via output feedback are presented. An example is presented illustrating the application of the algorithm. 相似文献
18.
Lp-Lq Estimate of the Stokes Operator and Navier–Stokes Flows in the Exterior of a Rotating Obstacle
We consider the motion of a viscous fluid filling the whole three-dimensional space exterior to a rotating obstacle with constant
angular velocity. We develop the L
p
-L
q
estimates and the similar estimates in the Lorentz spaces of the Stokes semigroup with rotation effect. We next apply them
to the Navier–Stokes equation to prove the global existence of a unique solution which goes to a stationary flow as t → ∞ with some definite rates when both the stationary flow and the initial disturbance are sufficiently small in L
3,∞ (weak-L
3 space). 相似文献
19.
Tobias Hansel 《Journal of Mathematical Fluid Mechanics》2011,13(3):405-419
We consider the equations of Navier–Stokes modeling viscous fluid flow past a moving or rotating obstacle in
\mathbb Rd{\mathbb R^d} subject to a prescribed velocity condition at infinity. In contrast to previously known results, where the prescribed velocity
vector is assumed to be parallel to the axis of rotation, in this paper we are interested in a general outflow velocity. In
order to use L
p
-techniques we introduce a new coordinate system, in which we obtain a non-autonomous partial differential equation with an
unbounded drift term. We prove that the linearized problem in
\mathbb Rd{\mathbb R^d} is solved by an evolution system on
Lps(\mathbb Rd){L^p_{\sigma}(\mathbb R^d)} for 1 < p < ∞. For this we use results about time-dependent Ornstein–Uhlenbeck operators. Finally, we prove, for p ≥ d and initial data
u0 ? Lps(\mathbb Rd){u_0\in L^p_{\sigma}(\mathbb R^d)}, the existence of a unique mild solution to the full Navier–Stokes system. 相似文献
20.
We study the asymptotic behavior of L
∞
weak-entropy solutions to the compressible Euler equations with damping and vacuum. Previous works on this topic are mainly
concerned with the case away from the vacuum and small initial data. In the present paper, we prove that the entropy-weak
solution strongly converges to the similarity solution of the porous media equations in L
p
(R) (2≤p<∞) with decay rates. The initial data can contain vacuum and can be arbitrary large. A new approach is introduced to control
the singularity near vacuum for the desired estimates.
(Accepted August 31, 2002) Published online January 9, 2003
Communicated by C. M. Dafermos 相似文献