Mathematical Aspects of Physics with Non-Self-Adjoint Operators: 10 Years After / Les aspects mathématiques de la physique avec les opérateurs non-auto-adjoints: 10 ans après

Collection Mathematical Aspects of Physics with Non-Self-Adjoint Operators: 10 Years After / Les aspects mathématiques de la physique avec les opérateurs non-auto-adjoints: 10 ans après

Organisateur(s) Boulton, Lyonell ; Krejcirik, David ; Siegl, Petr

Date(s) 01/02/2021 - 05/02/2021

URL associée https://conferences.cirm-math.fr/2153.html

00:00:00 / 00:00:00

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Complications making amplitude equations in fluid mechanics

De Catherine Drysdale

Ginzburg-Landau equation

Owing to the interaction between modes, difficulties arise in creating amplitude equations where non-normality and nonlinearity is present in the original system. For example, if amplitude equations are made via weakly nonlinear analysis, then approximating via the critical mode only (least stable eigenvalue) does not work at higher orders where the mixing of the modes needs to be taken into consideration. However, using a different homogenisation technique, namely stochastic singular perturbation theory of authors like Papanicalaou , Blömker & al, where noise is applied to the stable modes only, then the linear operator in question is no longer non-self-adjoint. Although, the difficulty of the problem shifts to showing that we can use a Rigged Hilbert Space construction. If the original problem in a Hilbert space H. We force the main operator of our problem to be Hilbert-Schmidt by choosing our noise in a dense subspace S of H. We demonstrate this on the Complex-Ginsburg-Landau equation with cubic nonlinearity.

Informations sur la vidéo

Date de captation 26/03/2020
Date de publication 26/02/2021
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Audience Chercheurs
Réalisateur(s) Guillaume Hennenfent
Format MP4

Données de citation

DOI 10.24350/CIRM.V.19711503
Citer cette vidéo Drysdale, Catherine (26/03/2020). Complications making amplitude equations in fluid mechanics. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19711503
URL https://dx.doi.org/10.24350/CIRM.V.19711503

Domaine(s)

Physique mathématique

Bibliographie

PAPANICOLAOU, George C. Some probabilistic problems and methods in singular perturbations. The Rocky Mountain Journal of Mathematics, 1976, p. 653-674. - https://www.jstor.org/stable/44240337
BLÖMKER, Dirk et MOHAMMED, Wael W. Amplitude equations for SPDEs with cubic nonlinearities. Stochastics An International Journal of Probability and Stochastic Processes, 2013, vol. 85, no 2, p. 181-215. - https://doi.org/10.1080/17442508.2011.624628

Codes MSC

76E09 Stability and instability of nonparallel flows

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