I am a PhD student in Maths, in the PDEs team, with a co-tutorial thesis under the supervision of Daniele Del Santo (Università degli Studi di Trieste, Trieste, Italy) and Francesco Fanelli (Institut Camille Jordan, Lyon, France). The aim of my PhD thesis is to investigate some stability and instability issues in the mathematical theory of fast rotating fluids. In the first part of the project, the goal was to investigate the interplay of stratification and fast rotation in the dynamics of geophysical flows, focusing on the case of the compressible Navier-Stokes-Fourier system, following recent results on multi-scale analysis by Feireisl and Novotný. We considered multi-scale asymptotic limit for the Navier-Stokes-Fourier system with strong Coriolis force, taking into account the presence of centrifugal and gravitational forces. In the second part of the project, we will focus on the study of hyperbolic problems and, in particular, of the incompressible Euler equations with density variation and, in addition, the Coriolis force. We will study the stability of "tangential regularity" solutions with respect to the (small) Rossby number.
Page at UniTs: web.units.it/dottorato/esfm/en/content/sbaiz-gabriele
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Università degli Studi di Trieste
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