Lorenz方程同窗轨的存在参数

本文讨论了Lorenz方程,得到存在同窗轨的参数区,用新的方法分析了混沌现象的起因。     

Navier-Stokes方程五模类Lorenz方程组的动力学行为及数值仿真

本文对平面正方形区域上不可压缩的Navier-Stokes方程,进行傅立叶展开后,截断得到五模类Lorenz方程组.给出了该方程组定常解及其稳定性的讨论,证明了该方程组吸引子的存在性,并对其全局稳定性进行了分析和讨论,数值模拟了雷诺数在一定范围内变化时,类Lorenz方程组的动力学行为.     

仅有y-分量耦合的非恒同Lorenz系统的渐近同步

本文考虑外部耦合格式为n×n阶实对称不可约,行和为零且对角线以外的元素非正的矩阵,内部耦合格式为仅有y-分量参与耦合的非恒同Lorenz格点系统的渐近同步.在系统解一致有界耗散的基础上采用常数变易法证明了当耦合强度足够大时仅有y-分量参与耦合的非恒同Lorenz格点系统的解出现渐近同步,即系统解的任意两个对应分量的差在时间趋向于无穷时是一个小的有界量.     

仅有x-分量耦合的非恒同Lorenz系统的渐近同步

考虑外部耦合格式为n×x阶实对称不可约,行和为零且对角线以外的元素非正的矩阵,内部耦合格式为仅有x-分量参与耦合的非恒同Lorenz格点系统的渐近同步.运用Lyapunov稳定性理论讨论系统解的一致有界耗散性.并在此基础上采用Cauchy-Schwaxz不等式证明当耦合强度足够大时仅有x-分量参与耦合的非恒同Lorenz格点系统的解出现渐近同步,即系统解的任意两个对应分量的差在时间趋向于无穷时是一个小的有界量.     

Large Deviations for Stochastic Volterra Equations in the Plane

We prove a Large Deviation Principle for the family of solutions of Volterra equations in the plane obtained by perturbation of the driving white noise. One of the motivations for the study of such class of equations is provided by non-linear hyperbolic stochastic partial differential equations appearing in the construction of some path-valued processes on manifolds. The proof uses the method developped by Azencott for diffusion processes. The main ingredients are exponential inequalities for different classes of two-parameter stochastic integrals; these integrals are related to the representation of the stochastic term in the differential equation as a representable semimatringale.     

Large Deviations for Multivalued Stochastic Differential Equations

We prove a large deviation principle of Freidlin–Wentzell type for multivalued stochastic differential equations with monotone drifts that in particular contain a class of SDEs with reflection in a convex domain.     

Global Large Solutions to the Navier-Stokes-Nernst-Planck-Poisson Equations

In this article, we obtain a new wellposedness result to the \(d\)-dimensional Navier-Stokes-Nernst-Planck-Poisson equations. Our result implies that, if the initial charge densities of a negatively and positively charged species are close enough, we can get global solutions only needing smallness condition imposed on initial velocity. The structure coming from equations and the weighted Chemin-Lerner type space are crucial in our arguments.     

一类修正的Navier-Stokes方程的长时间性态

该文主要讨论,Rⁿ上一类修正的 Navier-Stokes 方程弱解的长时间性态, 通过进一步改进Fourier分解方法, 得到了当初速度u_0∈ L² ∩L¹时其弱解在L² 范数下的最优衰减率为 (1+t)^n/4 同时该文也给出了修正的Navier-Stokes 方程与经典Navier-Stokes 方程的误差估计.     

Large Deviations for Stochastic Tamed 3D Navier-Stokes Equations

In this paper, using weak convergence method, we prove a large deviation principle of Freidlin-Wentzell type for the stochastic tamed 3D Navier-Stokes equations driven by multiplicative noise, which was investigated in (Röckner and Zhang in Probab. Theory Relat. Fields 145(1–2), 211–267, 2009).     

The Asymptotic Expansion of Solutions for the Navier-Stokes Equations with Large Parameters

In this paper, we decomposite the coefficient matrix of the Navier-Stokes equations with large parameter in λ power. By factor analysis and energy estimation, the long time existence and asymptotic expansion of the solution tor the system are obtained. Key words Navier-Stokes equations; expansion; approximation.     

Block Krylov Subspace Methods for Large Algebraic Riccati Equations

In the present paper, we present numerical methods for the computation of approximate solutions to large continuous-time and discrete-time algebraic Riccati equations. The proposed methods are projection methods onto block Krylov subspaces. We use the block Arnoldi process to construct an orthonormal basis of the corresponding block Krylov subspace and then extract low rank approximate solutions. We consider the sequential version of the block Arnoldi algorithm by incorporating a deflation technique which allows us to delete linearly and almost linearly dependent vectors in the block Krylov subspace sequences. We give some theoretical results and present numerical experiments for large problems.     

Block Krylov Subspace Methods for Solving Large Sylvester Equations

In the present paper, we propose block Krylov subspace methods for solving the Sylvester matrix equation AX–XB=C. We first consider the case when A is large and B is of small size. We use block Krylov subspace methods such as the block Arnoldi and the block Lanczos algorithms to compute approximations to the solution of the Sylvester matrix equation. When both matrices are large and the right-hand side matrix is of small rank, we will show how to extract low-rank approximations. We give some theoretical results such as perturbation results and bounds of the norm of the error. Numerical experiments will also be given to show the effectiveness of these block methods.     

Large Deviations for Quasilinear Parabolic Stochastic Partial Differential Equations

Potential Analysis - In this paper, we establish the Freidlin-Wentzell’s large deviations for quasilinear parabolic stochastic partial differential equations with multiplicative noise, which...     

Hysteresis,Period Doubling,and Intermittency at High Prandtl Number in the Lorenz Equations

We analyse a recently derived difference equation for the Lorenz equations, and thereby predict previously observed phenomena of period doubling and intermittent transitions. We also predict a hysteretic effect in such transitions, and give quantitative approximations to the bifurcation curves in (r, σ) parameter space. These are in agreement with the results of direct numerical simulation.     

Energy cycle for the Lorenz attractor

In this paper we identify an energetic cycle in the Lorenz-63 system through its Lie–Poisson structure. A new geometrical view of this Lorenz system is presented and sheds light on its energetic properties by recovering its Hamiltonian structure and the associated Casimir. It is shown that this approach gives notable physical insight on the dynamical behaviour of the system. A link between energetics and chaotic properties has been found and specific inequalities, involving conversion terms, have been identified. Traps and jumps between the lobes are studied and benefits of our formalism to capture predictability-energy connections are discussed.     

Large Deviation Principle for the Two-dimensional Stochastic Navier-Stokes Equations with Anisotropic Viscosity

Acta Mathematicae Applicatae Sinica, English Series - In this paper we establish the large deviation principle for the the two-dimensional stochastic Navier-Stokes equations with anisotropic...     

Nonradial Large Solutions of Sublinear Elliptic Equations

We show that the equation Δu = p(x)f(u) has a positive solution on R ^N , N ≥ 3, satisfying <artwork name="GAPA31011ei1"> <artwork name="GAPA31011ei2"> if and only if <artwork name="GAPA31011ei3"> when ψ(r) = min{p(x): |x| = r}. The nondecreasing continuous function f satisfies f(0) = 0, f (s) > 0 for s > 0, and sup _{s ≥ 1} f(s)/s<∞, and the nonnegative continuous function p is required to be asymptotically radial. This extends previous results which required the function p to be constant or radial.