Finite-dimensional Pullback Attractors for Non-autonomous Newton–Boussinesq Equations in Some Two-dimensional Unbounded Domains

2014 ◽  
Vol 62 (3) ◽  
pp. 265-289
Author(s):  
Cung The Anh ◽  
Dang Thanh Son
Keyword(s):  
Unbounded Domains ◽  
Boussinesq Equations ◽  
Two Dimensional ◽  
Pullback Attractors ◽  
Finite Dimensional

Integrable two-dimensional dynamical systems and the characteristic Lie algebras

2007 ◽  
Vol 5 ◽  
pp. 195-200
Author(s):  
A.V. Zhiber ◽  
O.S. Kostrigina
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Second Order ◽  
System Of Equations ◽  
Two Dimensional ◽  
Finite Dimensional ◽  
Dimensional Dynamical System

In the paper it is shown that the two-dimensional dynamical system of equations is Darboux integrable if and only if its characteristic Lie algebra is finite-dimensional. The class of systems having a full set of fist and second order integrals is described.

scholarly journals Toward understanding the multiscale spatial spectrum of solar convection

2012 ◽  
Vol 8 (S294) ◽  
pp. 361-363
Author(s):  
A. V. Getling ◽  
O. S. Mazhorova ◽  
O. V. Shcheritsa
Keyword(s):  
Convective Instability ◽  
Convective Flow ◽  
Large Scale ◽  
Fluid Layer ◽  
Boussinesq Equations ◽  
Spatial Spectrum ◽  
Small Scale ◽  
Two Dimensional ◽  
Solar Convection

AbstractConvection is simulated numerically based on two-dimensional Boussinesq equations for a fluid layer with a specially chosen stratification such that the convective instability is much stronger in a thin subsurface sublayer than in the remaining part of the layer. The developing convective flow has a small-scale component superposed onto a basic large-scale roll flow.

Similarity reductions and exact solutions for two-dimensional Euler–Boussinesq equations

2019 ◽  
Vol 33 (27) ◽  
pp. 1950328
Author(s):  
En Gui Fan ◽  
Man Wai Yuen
Keyword(s):  
Exact Solutions ◽  
Stream Function ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Boussinesq Equations ◽  
Two Dimensional ◽  
Similarity Reduction ◽  
Wave Solutions ◽  
Similarity Reductions

In this paper, by introducing a stream function and new coordinates, we transform classical Euler–Boussinesq equations into a vorticity form. We further construct traveling wave solutions and similarity reduction for the vorticity form of Euler–Boussinesq equations. In fact, our similarity reduction provides a kind of linearization transformation of Euler–Boussinesq equations.

scholarly journals The Finite-Dimensional Uniform Attractors for the Nonautonomous g-Navier-Stokes Equations

2009 ◽  
Vol 2009 ◽  
pp. 1-17 ◽  
Author(s):  
Delin Wu
Keyword(s):  
Fractal Dimension ◽  
Bounded Domain ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Uniform Attractor ◽  
Navier Stokes Equations ◽  
Finite Dimensional ◽  
Uniform Attractors

We consider the uniform attractors for the two dimensional nonautonomous g-Navier-Stokes equations in bounded domain . Assuming , we establish the existence of the uniform attractor in and . The fractal dimension is estimated for the kernel sections of the uniform attractors obtained.

Pullback attractors for a two-dimensional Navier–Stokes model in an infinite delay case

2011 ◽  
Vol 74 (5) ◽  
pp. 2012-2030 ◽  
Author(s):  
Pedro Marín-Rubio ◽  
José Real ◽  
José Valero
Keyword(s):  
Infinite Delay ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Pullback Attractors
Sign in / Sign up

Export Citation Format

Share Document