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Displaying similar documents to “On the Paneitz energy on standard three sphere”

Some special solutions of self similar type in MHD, obtained by a separation method of variables

Michel Cessenat, Philippe Genta (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We use a method based on a separation of variables for solving a first order partial differential equations system, using a very simple modelling of MHD. The method consists in introducing three unknown variables , , in addition to the time variable and then in searching a solution which is separated with respect to and only. This is allowed by a very simple relation, called a “metric separation equation”, which...

On a model of rotating superfluids

Sylvia Serfaty (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider an energy-functional describing rotating superfluids at a rotating velocity , and prove similar results as for the Ginzburg-Landau functional of superconductivity: mainly the existence of branches of solutions with vortices, the existence of a critical above which energy-minimizers have vortices, evaluations of the minimal energy as a function of , and the derivation of a limiting free-boundary problem.

Conjugate-cut loci and injectivity domains on two-spheres of revolution

Bernard Bonnard, Jean-Baptiste Caillau, Gabriel Janin (2013)

ESAIM: Control, Optimisation and Calculus of Variations

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In a recent article [B. Bonnard, J.-B. Caillau, R. Sinclair and M. Tanaka, 26 (2009) 1081–1098], we relate the computation of the conjugate and cut loci of a family of metrics on two-spheres of revolution whose polar form is  = d  + ()d to the period mapping of the -variable. One purpose of this article is to use this relation to evaluate the cut and conjugate loci for a family of metrics arising as a deformation of the round sphere and to determine the...

Shape optimization problems for metric graphs

Giuseppe Buttazzo, Berardo Ruffini, Bozhidar Velichkov (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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): ∈ 𝒜, ℋ() = }, where ℋ ,,  }  ⊂ R . The cost functional ℰ() is the Dirichlet energy of defined through the Sobolev functions on vanishing on the points . We analyze the existence of a solution in both the families of connected sets and of metric graphs. At the end, several explicit examples are discussed.