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1.
Introduction WeconsidertheperturbedcouplednonlinearSchr dingerequations(CNLS)iq1t=q1xx 2[|q1|2 |q2|2-ω2]q1 iε(^D1q1-r1),iq2t=q2xx 2[|q1|2 |q2|2-ω2]q2 iε(^D2q2-r2),(1)whereqjis2πperiodicandeveninx.rjisconstant,^Djisboundeddissipativeoperatorand assumedtotaketheform^Djqj=-αjqj βj^Bqj,(2)αjandβjarepositiveconstants,j=1,2.^BisaFouriertruncationofLaplaceoperator xx,i.e.,^Bcos(kx)=-k2cos(kx),k0isasmallperturbation parameter.Th… 相似文献
2.
The dynamical character for a perturbed coupled nonlinear Schrodinger system with periodic boundary condition was studied. First, the dynamical character of perturbed and unperturbed systems on the invariant plane was analyzed by the spectrum of the linear operator. Then the existence of the locally invariant manifolds was proved by the singular perturbation theory and the fixed-point argument. 相似文献
3.
The long time behavior of solution of the Hasegawa-Mima equation with dissipation term was considered. The global attractor problem of the Hasegawa-Mima equation with initial periodic boundary condition was studied. Applying the uniform a priori estimates method, the existence of global attractor of this problem was proved, and also the dimensions of the global attractor was estimated. 相似文献
4.
5.
研究了一类带随机初值并且由分数次Brownian运动驱动的随机偏微分方程.借助于Kolmogorov准则,建立了整体Lipschitz条件下此类随机偏微分方程的一个解.同时证明了局部Lipschitz条件下整体解的存在性. 相似文献
6.
This paper deals with the stochastic 2D Boussinesq equations with partial viscosity. This is a coupled system of Navier-Stokes/Euler equations and the transport equation for temperature under additive noise. Global well-posedness result of this system under partial viscosity is proved by using classical energy estimates method. 相似文献
7.
非线性Schr(o|¨)dinger方程是非线性科学领域的最基本的方程之一,本文综述该方程的两个有趣的现象:怪波和Bose-Einstein凝聚,最后提出一些相关的公开问题. 相似文献
8.
A class of time fractional partial differential equations is considered, which in- cludes a time fractional diffusion equation, a time fractional reaction-diffusion equation, a time fractional advection-diffusion equation, and their corresponding integer-order partial differential equations. The fundamental solutions to the Cauchy problem in a whole-space domain and the signaling problem in a half-space domain are obtained by using Fourier- Laplace transforms and their inverse transforms. The appropriate structures of the Green functions are provided. On the other hand, the solutions in the form of a series to the initial and boundary value problems in a bounded-space domain are derived by the sine- Laplace or cosine-Laplace transforms. Two examples are presented to show applications of the present technique. 相似文献
9.
Blow-up and Global Smooth Solutions for Incompressible Three-Dimensional Navier--Stokes Equations 下载免费PDF全文
We present some explicit self-similar blow-up solutions and some other solutions of the incompressible threedimensional Navier Stokes equations. These solutions indicate that in C^∞ the solution of Navier-Stokes equations does not always tend to a solution of Euler equations. 相似文献
10.
In this paper,the convergence rates of solutions to the three-dimensional turbulent flow equations are considered.By combining the Lp-Lq estimate for the linearized equations and an elaborate energy method,the convergence rates are obtained in various norms for the solution to the equilibrium state in the whole space when the initial perturbation of the equilibrium state is small in the H3-framework.More precisely,the optimal convergence rates of the solutions and their first-order derivatives in the L2-norm are obtained when the Lp-norm of the perturbation is bounded for some p ∈[1,6/5). 相似文献