共查询到20条相似文献,搜索用时 46 毫秒
1.
Yoshikazu Giga Katsuya Inui Alex Mahalov Shin’ya Matsui Jürgen Saal 《Archive for Rational Mechanics and Analysis》2007,186(2):177-224
We prove time local existence and uniqueness of solutions to a boundary layer problem in a rotating frame around the stationary
solution called the Ekman spiral. We choose initial data in the vector-valued homogeneous Besov space for 2 < p < ∞. Here the L
p
-integrability is imposed in the normal direction, while we may have no decay in tangential components, since the Besov space
contains nondecaying functions such as almost periodic functions. A crucial ingredient is theory for vector-valued homogeneous
Besov spaces. For instance we provide and apply an operator-valued bounded H
∞-calculus for the Laplacian in for a general Banach space . 相似文献
2.
Under certain assumptions on f and g we prove that positive, global and bounded solutions u of the non-autonomous heat equation
in
(N ≥ 3) converge to a steady state.
Dedicated to Prof. Pavol Brunovsky on the occasion of his 70th birthday. 相似文献
3.
In this paper we solve the stationary Oseen equations in
. The behavior of the solutions at infinity is described by setting the problem in weighted Sobolev spaces including anisotropic
weights. The study is based on a Lp theory for 1 < p < ∞. 相似文献
4.
A Jordan Curve Spanned by a Complete Minimal Surface 总被引:1,自引:0,他引:1
Francisco Martín Nikolai Nadirashvili 《Archive for Rational Mechanics and Analysis》2007,184(2):285-301
In this paper we construct complete (conformal) minimal immersions
which admit continuous extensions to the closed disk,
. Moreover,
is a homeomorphism and
is a (non-rectifiable) Jordan curve with Hausdorff dimension 1.
It turns out that the set of Jordan curves
constructed by the above procedure is dense in the space of Jordan curves of
with the Hausdorff metric. 相似文献
5.
Changyou Wang 《Archive for Rational Mechanics and Analysis》2008,188(2):351-369
For any compact n-dimensional Riemannian manifold (M, g) without boundary, a compact Riemannian manifold without boundary, and 0 < T ≦ +∞, we prove that for n ≧ 4, if u : M × (0, T] → N is a weak solution to the heat flow of harmonic maps such that , then u ∈C
∞(M × (0, T], N). As a consequence, we show that for n ≧3, if 0 < T < +∞ is the maximal time interval for the unique smooth solution u ∈C
∞(M × [0, T), N) of (1.1), then blows up as t ↑ T. 相似文献
6.
Florin Diacu Juan Manuel Sánchez-Cerritos Shuqiang Zhu 《Journal of Dynamics and Differential Equations》2018,30(1):209-225
We prove that the fixed points of the curved 3-body problem and their associated relative equilibria are Lyapunov stable if the solutions are restricted to \({\mathbb {S}}^1\), but unstable if the bodies are considered in \({\mathbb {S}}^2\). 相似文献
7.
The thermal decomposition of CS2 highly diluted in Ar was studied behind reflected shock waves by monitoring time-dependent absorption profiles of S(3P) and S(1D) using atomic resonance absorption spectroscopy (ARAS). The rate coefficient of the reaction:
相似文献
8.
We study the global attractor of the non-autonomous 2D Navier–Stokes (N.–S.) system with singularly oscillating external force of the form . If the functions g
0(x, t) and g
1 (z, t) are translation bounded in the corresponding spaces, then it is known that the global attractor is bounded in the space H, however, its norm may be unbounded as since the magnitude of the external force is growing. Assuming that the function g
1 (z, t) has a divergence representation of the form where the functions (see Section 3), we prove that the global attractors of the N.–S. equations are uniformly bounded with respect to for all . We also consider the “limiting” 2D N.–S. system with external force g
0(x, t). We have found an estimate for the deviation of a solution of the original N.–S. system from a solution u
0(x, t) of the “limiting” N.–S. system with the same initial data. If the function g
1 (z, t) admits the divergence representation, the functions g
0(x, t) and g
1 (z, t) are translation compact in the corresponding spaces, and , then we prove that the global attractors converges to the global attractor of the “limiting” system as in the norm of H. In the last section, we present an estimate for the Hausdorff deviation of from of the form: in the case, when the global attractor is exponential (the Grashof number of the “limiting” 2D N.–S. system is small).
相似文献
9.
In this paper, we establish the local well-posedness for the Cauchy problem of a simplified version of hydrodynamic flow of nematic liquid crystals in ${\mathbb{R}^3}$ for any initial data (u 0, d 0) having small ${L^{3}_{\rm uloc}}$ -norm of ${(u_{0}, \nabla d_{0})}$ . Here ${L^{3}_{\rm uloc}(\mathbb{R}^3)}$ is the space of uniformly locally L 3-integrable functions. For any initial data (u 0, d 0) with small ${\|(u_0, \nabla d_0)\|_{L^{3}(\mathbb{R}^3)}}$ , we show that there exists a unique, global solution to the problem under consideration which is smooth for t > 0 and has monotone deceasing L 3-energy for ${t \geqq 0}$ . 相似文献
10.
Role of the Pressure for Validity of the Energy Equality for Solutions of the Navier–Stokes Equation
Igor Kukavica 《Journal of Dynamics and Differential Equations》2006,18(2):461-482
We prove that a weak solution
of the Navier–Stokes system satisfies the energy equality if the associated pressure is locally square integrable. A similar statement is shown to hold for the Euler system. 相似文献
11.
Existence and uniqueness of local strong solutions and small global strong solutions of an evolutionary system of magnetohydrodynamics type in the whole
space will be proved in this paper. Moreover, some decay properties of the strong solutions will also be presented. 相似文献
12.
Yoichi Mito Thomas J. Hanratty Paulo Zandonade Robert D. Moser 《Flow, Turbulence and Combustion》2007,79(2):175-189
This paper uses direct numerical simulations (DNS) of turbulent flow in a channel at (Del álamo, Jiménez, Zandonade, Moser J Fluid Mech 500:135–144, 2004) to provide a picture of the turbulent structures making large contributions to the Reynolds shear stress.
Considerable work of this type has been done for the viscous wall region at smaller , for which a log-layer does not exist. Recent PIV measurements of turbulent velocity fluctuations in a plane parallel to
the direction of flow have emphasized the dominant contribution of large scale structures in the outer flow. This prompted
Hanratty and Papavassiliou (The role of wall vortices in producing turbulence. In: Panton, R.L. (ed) Self-sustaining Mechanism of Wall Turbulence. Computational Mechanics Publications, Southampton, pp. 83–108, 1997) to use DNS at to examine these structures in a plane perpendicular to the direction of flow. They identified plumes which extend from the
wall to the center of a channel. The data at are used to explore these results further, to examine the structure of the log-layer, and to test present notions about the
viscous wall layer. 相似文献
13.
Peter Hornung 《Archive for Rational Mechanics and Analysis》2011,199(3):1015-1067
Let \({S\subset\mathbb{R}^2}\) be a bounded Lipschitz domain and denote by \({W^{2,2}_{\text{iso}}(S; \mathbb{R}^3)}\) the set of mappings \({u\in W^{2,2}(S;\mathbb{R}^3)}\) which satisfy \({(\nabla u)^T(\nabla u) = Id}\) almost everywhere. Under an additional regularity condition on the boundary \({\partial S}\) (which is satisfied if \({\partial S}\) is piecewise continuously differentiable), we prove that the strong W 2,2 closure of \({W^{2,2}_{\text{iso}}(S; \mathbb{R}^3)\cap C^{\infty}(\overline{S};\mathbb{R}^3)}\) agrees with \({W^{2,2}_{\text{iso}}(S; \mathbb{R}^3)}\). 相似文献
14.
Vincenzo Ambrosio Hichem Hajaiej 《Journal of Dynamics and Differential Equations》2018,30(3):1119-1143
This paper is concerned with the following fractional Schrödinger equation 相似文献
$$\begin{aligned} \left\{ \begin{array}{ll} (-\Delta )^{s} u+u= k(x)f(u)+h(x) \text{ in } \mathbb {R}^{N}\\ u\in H^{s}(\mathbb {R}^{N}), \, u>0 \text{ in } \mathbb {R}^{N}, \end{array} \right. \end{aligned}$$ 15.
V. E. Slyusarchu 《Nonlinear Oscillations》2002,5(3):372-378
We find necessary and sufficient conditions for the nonlinear difference operator $\left( {\mathcal{D}x} \right)\left( t \right) = x\left( {t + 1} \right) - f\left( {x\left( t \right)} \right)$ $t \in \mathbb{R}$ , where $f:\mathbb{R} \to \mathbb{R}$ is a continuous function, to have the inverse in the space of functions bounded and continuous on $\mathbb{R}$ . 相似文献
16.
Journal of Dynamics and Differential Equations - Let $$h:V\subset {\mathbb {R}}^{2}\longrightarrow {\mathbb {R}}^{2}$$ be an embedding. The aim of this paper is to analyze the dynamical behavior of... 相似文献
17.
We consider the Cauchy problem for incompressible Navier–Stokes equations
with initial data in
, and study in some detail the smoothing effect of the equation. We prove that for T < ∞ and for any positive integers n and m we have
, as long as
stays finite. 相似文献
18.
S. M. Zhuk 《Nonlinear Oscillations》2007,10(4)
For a linear operator generated by the differential equation
19.
We show two examples of systems
in
with
such that |Zt| is strictly decreasing in time for any n but
as
. 相似文献
20.
Nonlinear Dynamics - The aim here is to study complex dynamical behavior in a new kind of non-smooth systems with two discontinuous boundaries in space $$\mathbb {R}^3$$ . This paper provides an... 相似文献
|