半空间上Boussinesq方程组弱解的L2衰减估计

主要研究外力函数f 满足一定条件时,半空间上Boussinesq 方程组当n≥3时弱解的L2衰减。先假设解光滑,给出了光滑解的一致L2衰减估计,再通过构造逼近解,对逼近解序列作一致衰减估计,取极限得到弱解的一致L2衰减估计。     

Boussinesq方程组弱解的衰减下界

本文利用Fourier分解方法研究Boussinesq方程组Cauchy问题弱解的L2衰减下界估计.     

Spatial decay bounds for the channel flow of the Boussinesq equations

In this paper, we consider the Boussinesq equations in a semi-infinite channel. We show that, under appropriate restrictions on the data, if the fluid velocity initially is small, the solution will tend exponentially to a transient laminar flow as the distance from the entry section tends to infinity. We also derive the explicit decay bounds.     

Optimal decay rates and small global solutions to the dissipative Boussinesq equation

This work is devoted to the small amplitude solutions for the initial value problem of the multidimensional dissipative Boussinesq equation. We firstly derive the pointwise estimates of the fundamental solutions by the energy method in the Fourier space. We give the asymptotic profiles of solutions to the corresponding linear problem to get the optimal decay rate for the -norm of solutions in all space dimensions. Under smallness assumptions on the initial data, we study the global existence and uniqueness of solutions by the contractive mapping principle in the solution spaces with time weighted norm.     

New solitary wave solutions for the bad Boussinesq and good Boussinesq equations

In this article, the sine–cosine, the standard tanh and the extended tanh methods has been used to obtain solutions of the bad Boussinesq and good Boussinesq equations. New solitions and periodic solutions are formally derived. The change of parameters, that will drastically change characteristics of the equation, is examined. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2009     

Local existence of strong solutions to the generalized Boussinesq equations

This paper deals with the local existence and uniqueness of strong solutions for the generalized Boussinesq equations with fractional dissipation. As a corollary, we establish some regularity criteria to guarantee smoothness of solutions.     

Solitary wave solutions of the one-dimensional Boussinesq equations

In this paper we derive an analytical solution of the one-dimensional Boussinesq equations, in the case of waves relatively long, with small amplitudes, in water of varying depth. To derive the analytical solution we first assume that the solution of the model has a prescribed wave form, and then we obtain the wave velocity, the wave number and the wave amplitude. Finally a specific application for some realistic values of wave parameters is given and a graphical presentation of the results is provided.      

Boussinesq方程组弱解的L~2衰减

利用付立叶分解方法(Fourier splitting method)研究Boussinesq方程组Cauchy问题弱解的L~2衰减.     

Exponential decay of the solutions for nonlinear multiharmonic equations

The purpose of this paper is to establish the exponential decay properties of the solutions for the nonlinear multiharmonic equation

where the condition plays the role of a boundary value condition.     

On the suitable weak solutions to the Boussinesq equations in a bounded domain

In this paper we construct the suitable weak solution for the initial-boundary value problem of the Boussinesq equations and obtain some properties for these solutions. Also in the case of a two dimensional space the uniqueness of weak solution is proved.     

An optimization‐based domain decomposition method for the Boussinesq equations

We study an optimization based domain decomposition method for the Boussinesq equations governing natural convection problems. Domain decomposition is cast into a constrained minimization problem for which the objective functional measures the jump in the dependent variables across the interface between solid and fluid subdomains. We showthat solutions of the minimization problem exist and derive an optimality system from which these solutions may be determined. Finite element approximations of the solutions of the optimality system are examined. The domain decomposition method is also reformulated as a nonlinear least‐squares problem and the results of some numerical experiments are given. © 2002 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 18: 1–25, 2002     

Analytical solution of variant Boussinesq equations

In this paper, analytic solutions of the variant Boussinesq equations are obtained by the homotopy analysis and the homotopy Pad methods. The obtained approximation using homotopy method contains an auxiliary parameter, which is a simple way to control and adjust the convergence region and rate of solution series. The approximation solutions by [m,m] homotopy Pad technique is often independent of auxiliary parameter , and this technique accelerates the convergence of the related series. Copyright © 2013 John Wiley & Sons, Ltd.     

Analytical solitary wave solutions for the nonlinear analogues of the Boussinesq and sixth-order modified Boussinesq equations

Using tanh function and polynomial function methods, analytical solitary wave solutions have been found for the nonlinear analogues of Boussinesq and sixth-order modified Boussinesq equations where the nonlinearity is in the time-derivative term.     

Error analysis for Galerkin POD approximation of the nonstationary Boussinesq equations

In this article, we study error estimates for approximate solutions of POD Galerkin type for the equations for the motion of a nonstationary viscous thermally conducting fluid in a bounded domain. Time discretization is based on backward Euler scheme. We study both the fully implicit and semi‐implicit versions of this scheme. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27 : 1639‐1665, 2011     

Serrin-type blow-up criteria for 3D Boussinesq equations

In this article, we consider the three-dimensional Boussinesq equations with the incompressibility condition. We obtain some Serrin-type regularity conditions for the three-dimensional Boussinesq equations.     

Blow‐up criteria of smooth solutions to the 3D Boussinesq equations

In this paper, we investigate three‐dimensional incompressible Boussinesq equations and establish some logarithmically improved blow‐up criteria of smooth solutions to the Cauchy problem for the incompressible Boussinesq equations. Copyright © 2011 John Wiley & Sons, Ltd.     

A staggered-grid numerical algorithm for the extended Boussinesq equations

A second-order accurate numerical scheme is developed to solve Nwogu’s extended Boussinesq equations. A staggered-grid system is introduced with the first-order spatial derivatives being discretized by the fourth-order accurate finite-difference scheme. For the time derivatives, the fourth-order accurate Adams predictor–corrector method is used. The numerical method is validated against available analytical solutions, other numerical results of Navier–Stokes equations, and experimental data for both 1D and 2D nonlinear wave transformation problems. It is shown that the new algorithm has very good conservative characteristics for mass calculation. As a result, the model can provide accurate and stable results for long-term simulation. The model has proven to be a useful modeling tool for a wide range of water wave problems.     

Periodic solutions in unbounded domains for the Boussinesq system

Assuming that the external forces of the system are small enough, the reference temperature being a periodic function, we study the existence, the uniqueness and the regularity of time-periodic solutions for the Boussinesq equations in several classes of unbounded domains of Rn. Our analysis is based on the framework of weak-Lp spaces.