Theses
Prelectura de Tesis: Stability analysis and special solutions in fluid mechanics models
Speaker: Miguel Martínez González (ICMAT)Advisor/s: Ángel CastroDate: Friday, 30 October 2026 - 10:00Place: Aula 520, departamento de matemáticas, UAM
Abstract:
Several nonlocal models have been proposed to better understand the incompressible Euler equations. Here we study special solutions of three such models: the inviscid surface quasi-geostrophic (SQG), De Gregorio, and Burgers–Hilbert equations. We prove the existence of homogeneous stationary solutions for SQG and stationary solutions for the generalized De Gregorio equation. We also establish the existence and spectral instability of a Burgers–Hilbert traveling wave, and the linear instability of all excited stationary states of the De Gregorio equation. The instability proofs combine spectral analysis with rigorous computer-assisted verification using interval arithmetic.
