\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

Attractor bifurcation theory and its applications to Rayleigh-Bénard convection

Abstract Related Papers Cited by
  • In this note, we present a fast communication of a new bifurcation theory for nonlinear evolution equations, and its application to Rayleigh-Bénard Convection. The proofs of the main theorems presented will appear elsewhere. The bifurcation theory is based on a new notion of bifurcation, called attractor bifurcation. We show that as the parameter crosses certain critical value, the system bifurcates from a trivial steady state solution to an attractor with dimension between $m$ and $m+1$, where $m+1$ is the number of eigenvalues crosses the imaginary axis. Based on this new bifurcation theory, we obtain a nonlinear theory for bifurcation and stability of the solutions of the Boussinesq equations, and the onset of the Rayleigh-Bénard convection. In particular, we show that the problem bifurcates from the trivial solution an attractor $\mathcal A_R$ when the Rayleigh number $R$ crosses the first critical Rayleigh number $R_c$ for all physically sound boundary conditions.
    Mathematics Subject Classification: 37L, 37G, 35Q, 58F, 76E, 76R.

    Citation:

    \begin{equation} \\ \end{equation}
  • 加载中
SHARE

Article Metrics

HTML views() PDF downloads(211) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return