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Cahn‐Hilliard Description of Secondary Flows of a Viscous Incompressible Fluid in an Unbounded Domain
Author(s) -
Schneider G.
Publication year - 1999
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/(sici)1521-4001(199909)79:9<615::aid-zamm615>3.0.co;2-7
Subject(s) - cahn–hilliard equation , compressibility , stability (learning theory) , mathematics , domain (mathematical analysis) , nonlinear system , action (physics) , instability , fourier transform , mathematical analysis , vibration , physics , classical mechanics , partial differential equation , mechanics , computer science , quantum mechanics , machine learning
A viscous incompressible fluid under the action of an external force in an infinite strip is considered. We are interested in the situation when the trivial ground state loses stability and a whole sideband of Fourier modes becomes unstable. In order to describe the bifurcating solutions a Cahn‐Hilliard equation can be derived. We show that the mathematical criteria are satisfied to call the Cahn‐Hilliard equation the amplitude or modulation equation of the system. Moreover, we give a nonlinear diffusive stability result for the marginal stable ground state.