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非線形解析セミナー

タイトル	Small-amplitude static periodic patterns at a fluid-ferrofluid interface
開催日時	2018年7月11日 17:15 ～ 18:15
主催者
講演者	Professor Mark Groves (University of Saarlandes)
場所	慶應義塾大学理工学部 14棟 631A/B (創想館 6階 ミーティング1A/1B)
内容	We establish the existence of static doubly periodic patterns (in particular rolls, squares and hexagons) on the free surface of a ferrofluid near onset of the Rosensweig instability, assuming a general (nonlinear) magnetisation law. A novel formulation of the ferrohydrostatic equations in terms of Dirichlet-Neumann operators for nonlinear elliptic boundary-value problems is presented. We demonstrate the analyticity of these operators in suitable function spaces and solve the ferrohydrostatic problem using an analytic version of Crandall-Rabinowitz local bifurcation theory. Criteria are derived for the bifurcations to be sub-, super- or transcritical with respect to a dimensionless physical parameter.
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