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Four Lectures in Semiclassical Analysis for Non Self-Adjoint Problems with Applications to Hydrodynamic Instability

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Pseudo-Differential Operators

Part of the book series: Lecture Notes in Mathematics ((LNMCIME,volume 1949))

Abstract

Our aim is to show how semi-classical analysis can be useful in questions of stability appearing in hydrodynamics. We will emphasize on the motivating examples and see how these problems can be solved or by harmonic approximation techniques used in the semi-classical analysis of the Schrödinger operator or by recently obtained semi-classical versions of estimates for operators of principal type (mainly subelliptic estimates). These notes correspond to an extended version of the course given at the school in Cetraro. We have in particularly kept the structure of these lectures with an alternance between the motivating examples and the presentation of the theory. Many of the results which are presented have been obtained in collaboration with Olivier Lafitte.

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Authors and Affiliations

  1. Laboratoire de Mathématiques, Université Paris-Sud, 91405, Orsay Cedex, France

    B. Helffer

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  1. B. Helffer
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Editors and Affiliations

  1. Dipartimento di Matematica, Universitá di Torino, Via Carlo Alberto 10, 10123, Torino, Italy

    Luigi Rodino

  2. Department of Mathematics and Statistics, York University, Keele Street 4700, M3J 1P3, Toronto, Ontario, Canada

    M. W. Wong

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Helffer, B. (2008). Four Lectures in Semiclassical Analysis for Non Self-Adjoint Problems with Applications to Hydrodynamic Instability. In: Rodino, L., Wong, M.W. (eds) Pseudo-Differential Operators. Lecture Notes in Mathematics, vol 1949. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68268-4_2

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