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Generalized Lieb-Thirring Inequalities and the Dimension of Attractors Associated to the Ginzburg-Landau p.d.e.

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Trends in Applications of Mathematics to Mechanics

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Abstract

This paper is concerned with the dimension of the global attractor that describes the long time behavior of the solutions to the 2D-Ginzburg-Landau partial differential equation. An upper bound on this dimension is derived via a generalized Lieb-Thirring inequality, while lower bounds follow from the classical (linear) stability analysis. As a matter of fact these bounds are of the same order and therefore optimal.

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Author information

Authors and Affiliations

  1. Laboratoire d’Analyse Numérique, CNRS et Université Paris-Sud, F-91405, Orsay Cédex, France

    J.-M. Ghidaglia

Authors
  1. J.-M. Ghidaglia
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Editor information

Editors and Affiliations

  1. Technological University, Mekelweg 2, NL-2628 CD, Delft, The Netherlands

    Johannes F. Besseling

  2. Mathematisch Instituut, Rijksuniversiteit Utrecht, Budapestlaan 6, NL-3584 CD, Utrecht, The Netherlands

    Wiktor Eckhaus

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© 1988 Springer-Verlag Berlin Heidelberg

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Ghidaglia, JM. (1988). Generalized Lieb-Thirring Inequalities and the Dimension of Attractors Associated to the Ginzburg-Landau p.d.e.. In: Besseling, J.F., Eckhaus, W. (eds) Trends in Applications of Mathematics to Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-73933-0_8

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  • DOI: https://doi.org/10.1007/978-3-642-73933-0_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-73935-4

  • Online ISBN: 978-3-642-73933-0

  • eBook Packages: Springer Book Archive

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