Bifurcation Theorems for the Model System of Bénard–Marangoni Convection

. We provide two bifurcation theorems, one of which guarantees the existence of nontrivial stationary solutions bifurcating from the basic heat conductive state in Bénard–Marangoni convection, another for bifurcating time periodic solution, under certain assumptions on the eigenvalues of the problem...

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Veröffentlicht in:Journal of mathematical fluid mechanics 2009-10, Vol.11 (3), p.383-406
Hauptverfasser: Nishida, Takaaki, Teramoto, Yoshiaki
Format: Artikel
Sprache:eng
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Zusammenfassung:. We provide two bifurcation theorems, one of which guarantees the existence of nontrivial stationary solutions bifurcating from the basic heat conductive state in Bénard–Marangoni convection, another for bifurcating time periodic solution, under certain assumptions on the eigenvalues of the problem obtained by linearization around the basic state. Since we reduce the problem to a fixed domain, the inhomogeneous terms of reduced equations and reduced boundary conditions contain the highest derivatives. To deal with these we apply the Lyapunov–Schmidt decomposition directly.
ISSN:1422-6928
1422-6952
DOI:10.1007/s00021-007-0263-9