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1.
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  
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.
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 uC (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 uC (M × [0, T), N) of (1.1), then blows up as tT.  相似文献   

6.
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.
D. Woiki  P. Roth 《Shock Waves》1994,4(2):95-99
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.
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.
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.
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.
This paper is concerned with the following fractional Schrödinger equation
$$\begin{aligned} \left\{ \begin{array}{ll} (-\Delta )^{s} u+u= k(x)f(u)+h(x) \text{ in } \mathbb {R}^{N}\\ u\in H^{s}(\mathbb {R}^{N}), \, u>0 \text{ in } \mathbb {R}^{N}, \end{array} \right. \end{aligned}$$
where \(s\in (0,1),N> 2s, (-\Delta )^{s}\) is the fractional Laplacian, k is a bounded positive function, \(h\in L^{2}(\mathbb {R}^{N}), h\not \equiv 0\) is nonnegative and f is either asymptotically linear or superlinear at infinity. By using the s-harmonic extension technique and suitable variational methods, we prove the existence of at least two positive solutions for the problem under consideration, provided that \(|h|_{2}\) is sufficiently small.
  相似文献   

15.
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.
For a linear operator generated by the differential equation
we prove that its graph is closed and determine the adjoint operator . For elements of the linear manifolds and , we propose an analog of the formula of integration by parts. We establish a criterion for the existence of a pseudosolution of the operator equation and formulate sufficient conditions for the normal solvability of the operator in terms of relations for blocks of the matrix C(t). The results obtained are illustrated by examples. __________ Translated from Neliniini Kolyvannya, Vol. 10, No. 4, pp. 464–480, October–December, 2007.  相似文献   

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.
Lu  Kai  Xu  Wenjing  Xiang  Qiaomin 《Nonlinear dynamics》2021,104(1):149-164
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   

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