Pseudospectra of semiclassical (pseudo-) differential operators

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Abstract

The pseudo-spectra (or spectral instability) of non-selfadjoint operators is a topic of current interest in applied mathematics. For example, in computational fluid dynamics it affects the study of the stability of laminar flows. In fact, even for the most basic flows, the computations entirely fails to predict what is observed in the experiments.

The explanation is that for non-normal operators the resolvent could be very large far away from the spectrum, which makes computation of the eigenvalues impossible. The occurence of ``false eigenvalues'' is due to the existence of quasi-modes, i.e., approximate local solutions
to the eigenvalue problem. The quasi-modes appear since the Nirenberg-Treves condition (Psi) is not satisfied for topological reasons.

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Ämnesklassifikation (UKÄ) – OBLIGATORISK

  • Matematik

Nyckelord

Originalspråkengelska
Sidor (från-till)384-415
TidskriftCommunications on Pure and Applied Mathematics
Volym57
Utgåva nummer3
StatusPublished - 2004
PublikationskategoriForskning
Peer review utfördJa