Tesi etd-05172025-122605 |
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Tipo di tesi
Tesi di dottorato di ricerca
Autore
ROVERI, LEONARDO
URN
etd-05172025-122605
Titolo
Stochastic Fluids - Theoretical Models and Machine Learning Applications
Settore scientifico disciplinare
MATH-03/B - Probabilità e statistica matematica
Corso di studi
MATEMATICA
Relatori
tutor Prof. Romito, Marco
Parole chiave
- cyclones
- dissipation
- euler
- fluid dynamics
- machine learning
- mathematicss
- probability
- quasi geostrophic
- rough paths
Data inizio appello
07/05/2025
Consultabilità
Completa
Riassunto
The thesis deals with various problems arising in the study of fluid dynamics. Its topics can be divided in two groups: problems presenting rougher terms than usual (either in the form of very irregular noise or in form of distributional terms) and problems arising in the context of climate studies. To the former group belong Chapters 1 and 3, respectively proving well-posedness of 2D Euler equations with transport noise of finite p-variation, p greater or equal than 2, and enhanced dissipation for an advection-diffusion equation when the transport term belongs to a distributional space. In the latter group, Chapters 2 proves existence of an invariant measure for a multi-layer quasi-geostrophic system, while in Chapter 4 a new methodology is developed to detect and locate Mediterranean cyclones based on statistical learning techniques.
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