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On the Nash-Moser Iteration Technique

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Recent Developments of Mathematical Fluid Mechanics

Part of the book series: Advances in Mathematical Fluid Mechanics ((AMFM))

Abstract

The aim of this work is to provide a brief presentation of the Nash-Moser iteration technique for the resolution of nonlinear equations, where the linearized equations admit estimates with a loss of regularity with respect to the given data.

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Notes

  1. 1.

    Similar smoothing operators \(S_{Y }(\theta ): Y _{0} \rightarrow Y _{\infty }:= \cap _{m\geq 0}Y _{m}\) are introduced as well.

  2. 2.

    Following Hörmander’s method [2, 11], in the sequel our iteration scheme will be a little more elaborated than in (5).

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Authors and Affiliations

  1. DICATAM, Section of Mathematics, University of Brescia, Via Valotti 9, 25133, Brescia, Italy

    Paolo Secchi

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  1. Paolo Secchi
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Correspondence to Paolo Secchi .

Editor information

Editors and Affiliations

  1. Universität of Zürich, Institut für Mathematik, Zürich, Switzerland

    Herbert Amann

  2. University of Tokyo, Graduate School of Mathematical Sciences, Tokyo, Japan

    Yoshikazu Giga

  3. Department of Mathematics, Waseda University, Tokyo, Japan

    Hideo Kozono

  4. Research Institute for Mathematical Sciences, Kyoto University Kitashirakawa, Kyoto, Japan

    Hisashi Okamoto

  5. Department of Mathematics, Waseda University, Tokyo, Japan

    Masao Yamazaki

Additional information

Dedicated to Professor Y. Shibata in occasion of his 60-th birthday

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Secchi, P. (2016). On the Nash-Moser Iteration Technique. In: Amann, H., Giga, Y., Kozono, H., Okamoto, H., Yamazaki, M. (eds) Recent Developments of Mathematical Fluid Mechanics. Advances in Mathematical Fluid Mechanics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0939-9_23

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