共查询到20条相似文献,搜索用时 15 毫秒
1.
G. Wolansky 《Archive for Rational Mechanics and Analysis》2001,156(3):205-230
Static solutions of the SO(3)-symmetric Vlasov-Einstein system are studied via a variational approach. For the constitutive
relation of the Emden-Fowler type φ(E,F)≡E
σ+ 1
F
k
we prove the existence of such solutions of sufficiently small mass-energy, provided 0<σ < k+3/2. These solutions are local minimizers of the energy-Casimir functional, subjected to a variational barrier.
Accepted July 16, 2000?Published online January 22, 2001 相似文献
2.
Xiao-Biao Lin 《Journal of Dynamics and Differential Equations》2007,19(4):1037-1074
We study the spectral and linear stability of Riemann solutions with multiple Lax shocks for systems of conservation laws.
Using a self-similar change of variables, Riemann solutions become stationary solutions for the system u
t
+ (Df(u) − x
I)u
x
= 0. In the space of O((1 + |x|)−η) functions, we show that if , then λ is either an eigenvalue or a resolvent point. Eigenvalues of the linearized system are zeros of the determinant of
a transcendental matrix. On some vertical lines in the complex plane, called resonance lines, the determinant can be arbitrarily small but nonzero. A C
0 semigroup is constructed. Using the Gearhart–Prüss Theorem, we show that the solutions are O(e
γ t
) if γ is greater than the real parts of the eigenvalues and the coordinates of resonance lines. We study examples where Riemann
solutions have two or three Lax-shocks.
Dedicated to Professor Pavol Brunovsky on his 70th birthday. 相似文献
3.
In this article we present a Ladyženskaja–Prodi–Serrin Criteria for regularity of solutions for the Navier–Stokes equation
in three dimensions which incorporates weak L
p
norms in the space variables and log improvement in the time variable. 相似文献
4.
In this paper a complex-order van der Pol oscillator is considered. The complex derivative Da±jbD^{\alpha\pm\jmath\beta}, with α,β∈R
+ is a generalization of the concept of integer derivative, where α=1, β=0. By applying the concept of complex derivative, we obtain a high-dimensional parameter space. Amplitude and period values
of the periodic solutions of the two versions of the complex-order van der Pol oscillator are studied for variation of these
parameters. Fourier transforms of the periodic solutions of the two oscillators are also analyzed. 相似文献
5.
Under assumptions on smoothness of the initial velocity and the external body force, we prove that there exists T
0 > 0, ν
0 > 0 and a unique continuous family of strong solutions u
ν
(0 ≤ ν < ν
0) of the Euler or Navier–Stokes initial-boundary value problem on the time interval (0, T
0). In addition to the condition of the zero flux, the solutions of the Navier–Stokes equation satisfy certain natural boundary
conditions imposed on curl
u
ν
and curl
2
u
ν
.
相似文献
6.
This paper concerns the regularity of a capillary graph (the meniscus profile of liquid in a cylindrical tube) over a corner
domain of angle α. By giving an explicit construction of minimal surface solutions previously shown to exist (Indiana Univ. Math. J. 50 (2001), no. 1, 411–441) we clarify two outstanding questions.
Solutions are constructed in the case α = π/2 for contact angle data (γ1, γ2) = (γ, π − γ) with 0 < γ < π. The solutions given with |γ − π/2| < π/4 are the first known solutions that are not C2 up to the corner. This shows that the best known regularity (C1, ∈) is the best possible in some cases. Specific dependence of the H?lder exponent on the contact angle for our examples is
given.
Solutions with γ = π/4 have continuous, but horizontal, normal vector at the corners in accordance with results of Tam (Pacific J. Math. 124 (1986), 469–482). It is shown that our examples are C0, β up to and including the corner for any β < 1.
Solutions with |γ − π/2| > π/4 have a jump discontinuity at the corner. This kind of behavior was suggested by numerical work
of Concus and Finn (Microgravity sci. technol. VII/2 (1994), 152–155) and Mittelmann and Zhu (Microgravity sci. technol. IX/1 (1996), 22–27). Our explicit construction, however, allows us to investigate the solutions quantitatively. For example,
the trace of these solutions, excluding the jump discontinuity, is C2/3. 相似文献
7.
For elliptic equations ε2Δu − V(x) u + f(u) = 0, x ∈ R
N
, N ≧ 3, we develop a new variational approach to construct localized positive solutions which concentrate at an isolated component
of positive local minimum points of V, as ε → 0, under conditions on f which we believe to be almost optimal.
An erratum to this article can be found at 相似文献
8.
José A. Carrillo Marco Di Francesco Giuseppe Toscani 《Archive for Rational Mechanics and Analysis》2006,180(1):127-149
We investigate the long time asymptotics in L1+(R) for solutions of general nonlinear diffusion equations ut = Δϕ(u). We describe, for the first time, the intermediate asymptotics for a very large class of non-homogeneous nonlinearities
ϕ for which long time asymptotics cannot be characterized by self-similar solutions. Scaling the solutions by their own second
moment (temperature in the kinetic theory language) we obtain a universal asymptotic profile characterized by fixed points
of certain maps in probability measures spaces endowed with the Euclidean Wasserstein distance d2. In the particular case of ϕ(u) ~ um at first order when u ~ 0, we also obtain an optimal rate of convergence in L1 towards the asymptotic profile identified, in this case, as the Barenblatt self-similar solution corresponding to the exponent
m. This second result holds for a larger class of nonlinearities compared to results in the existing literature and is achieved
by a variation of the entropy dissipation method in which the nonlinear filtration equation is considered as a perturbation
of the porous medium equation. 相似文献
9.
We consider the three-dimensional flow through an aperture in a plane either with a prescribed flux or pressure drop condition.
We discuss the existence and uniqueness of solutions for small data in weighted spaces and derive their complete asymptotic
behaviour at infinity. Moreover, we show that each solution with a bounded Dirichlet integral, which has a certain weak additional
decay, behaves like O(r
−2) as r=|x|→∞ and admits a wide jet region. These investigations are based on the solvability properties of the linear Stokes system
in a half space ℝ
+
3
. To investigate the Stokes problem in ℝ
+
3
, we apply the Mellin transform technique and reduce the Stokes problem to the determination of the spectrum of the corresponding
invariant Stokes-Beltrami operator on the hemisphere. 相似文献
10.
Piermarco Cannarsa Andrea Mennucci Carlo Sinestrari 《Archive for Rational Mechanics and Analysis》1997,140(3):197-223
The regularity of the gradient of viscosity solutions of first‐order Hamilton‐Jacobi equations is studied under a strict convexity assumption on H(t,x,⋅). Estimates on the discontinuity set of Du are derived. Such estimates imply that solutions of the above problem are smooth in the complement of a closed ℋ
n
‐rectifiable set. In particular, it follows that Du belongs to the classSBV, i.e., D
2
u$ is a measure with no Cantor part.
(Accepted February 12, 1996) 相似文献
11.
Yifeng Yu 《Archive for Rational Mechanics and Analysis》2006,182(1):153-180
In this paper, we prove that viscosity solutions of Aronsson equations are absolute minimizers in certain L
∞ variational problems. 相似文献
12.
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
13.
In this paper we study the two-dimensional hydrostatic Euler equations in a periodic channel. We prove the local existence
and uniqueness of H
s
solutions under the local Rayleigh condition. This extends Brenier’s (Nonlinearity 12(3):495–512, 1999) existence result by removing an artificial condition and proving uniqueness. In addition, we prove weak–strong uniqueness,
mathematical justification of the formal derivation and stability of the hydrostatic Euler equations. These results are based
on weighted H
s
a priori estimates, which come from a new type of nonlinear cancellation between velocity and vorticity. 相似文献
14.
We consider initial layers and uniqueness of weak entropy solutions to hyperbolic conservation laws through the scalar case.
The entropy solutions we address assume their initial data only in the sense of weak-star in L
∞ as t→0+ and satisfy the entropy inequality in the sense of distributions for t>0. We prove that, if the flux function has weakly genuine nonlinearity, then the entropy solutions are always unique and
the initial layers do not appear. We also discuss applications to the zero relaxation limit for hyperbolic systems of conservation
laws with relaxation.
Accepted: October 26, 1999 相似文献
15.
A closed-form model for the computation of temperature distribution in an infinitely extended isotropic body with a time-dependent
moving-heat sources is discussed. The temperature solutions are presented for the sources of the forms: (i) 01(t)=0
exp(−λt), (ii) 02(t) =0(t/t
*)exp(−λt), and 03(t)=0[1+a
cos(ωt)], where λ and ω are real parameters and t
* characterizes the limiting time. The reduced (or dimensionless) temperature solutions are presented in terms of the generalized
representation of an incomplete gamma function Γ(α,x;b) and its decomposition C
Γ and S
Γ. The solutions are presented for moving, -point, -line, and -plane heat sources. It is also demonstrated that the present
analysis covers the classical temperature solutions of a constant strength source under quasi-steady state situations.
Received on 13 June 1997 相似文献
16.
Zhi-Qiang Shao 《Journal of Elasticity》2010,98(1):25-64
In this paper, we investigate the asymptotic behavior of global classical solutions to the mixed initial-boundary value problem
with small BV data for linearly degenerate quasilinear hyperbolic systems with general nonlinear boundary conditions in the
half space {(t,x)|t≥0,x≥0}. Based on the existence result on the global classical solution, we prove that when t tends to the infinity, the solution approaches a combination of C
1 traveling wave solutions, provided that the C
1 norm of the initial and boundary data is bounded and the BV norm of the initial and boundary data is sufficiently small.
Applications to quasilinear hyperbolic systems arising in physics and mechanics, particularly to the system describing the
motion of the relativistic string in the Minkowski space-time R
1+n
, are also given. 相似文献
17.
Hyunseok Kim 《Archive for Rational Mechanics and Analysis》2009,193(1):117-152
We consider the stationary Navier–Stokes equations in a bounded domain Ω in R
n
with smooth connected boundary, where n = 2, 3 or 4. In case that n = 3 or 4, existence of very weak solutions in L
n
(Ω) is proved for the data belonging to some Sobolev spaces of negative order. Moreover we obtain complete L
q
-regularity results on very weak solutions in L
n
(Ω). If n = 2, then similar results are also proved for very weak solutions in with any q
0 > 2. We impose neither smallness conditions on the external force nor boundary data for our existence and regularity results. 相似文献
18.
Yan Guo 《Archive for Rational Mechanics and Analysis》2010,197(3):713-809
Boundaries occur naturally in kinetic equations, and boundary effects are crucial for dynamics of dilute gases governed by
the Boltzmann equation. We develop a mathematical theory to study the time decay and continuity of Boltzmann solutions for
four basic types of boundary conditions: in-flow, bounce-back reflection, specular reflection and diffuse reflection. We establish
exponential decay in the L
∞ norm for hard potentials for general classes of smooth domains near an absolute Maxwellian. Moreover, in convex domains,
we also establish continuity for these Boltzmann solutions away from the grazing set at the boundary. Our contribution is
based on a new L
2 decay theory and its interplay with delicate L
∞ decay analysis for the linearized Boltzmann equation in the presence of many repeated interactions with the boundary. 相似文献
19.
Xinyu He 《Journal of Mathematical Fluid Mechanics》2004,6(4):389-404
A self-similar solution of the three-dimensional (3d) incompressible Euler equations is defined byu(x,t) =U(y)/t*-t)
α, y = x/(t* ~ t)β,α,β> 0, whereU(y) satisfiesζU + βy. ΔU + U. VU + VP = 0,divU = 0. For α = β = 1/2, which is the limiting case of Leray’s self-similar Navier—Stokes equations, we prove the existence of(U,P) ε H3(Ω,R3 X R) in a smooth bounded domain Ω, with the inflow boundary data of non-zero vorticity. This implies the possibility that
solutions of the Euler equations blow up at a timet = t*, t* < +∞. 相似文献
20.
Saint-Venant's torsion of symmetric cylindrical bars consisting of two or four homogeneous phases is studied. A symmetric
section is meant that the cross section of the cylindrical bar possesses reflectional symmetry with respect to one or more
axes. Each constituent region may have different shear modulus. The idea of the analysis is to superimpose suitably reflected
potentials to obtain the torsion solution of the same composite section but with different moduli. For two-phase sections,
we show that, if the warping fields for a given symmetric section with phase shear moduli μ1 and μ2 are known a priori, then the warping fields for the same configuration but with a different set of constituent moduli μ1
′ and μ2
′ are readily found through simple linear superpositions. Further, suppose that the torsional rigidities T(μ1,μ2) and T(μ1
′,μ2
′) for any two sets of phase moduli can be measured by some experimental tests or evaluated through numerical procedures, then
the torsional rigidity for any other combinations of constituent moduli T(μ1
′′,μ2
′′) can be exactly determined without any recourse to the field solutions of governing differential equations. Similar procedures
can be applied to a 4-phase symmetric section. But the coefficients of superposition are only found for a few branches. Specifically,
we find that depending on the conditions of μ and μ′, admissible solutions can be divided into three categories. When the correspondence between the warping field is known to
exist, a link between the torsional rigidities can be established as well.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献