Ja és pública la resolució de la 4a edició del Barcelona Dynamical Systems Prize, un premi internacional ofert per la Societat Catalana de Matemàtiques, sota el patrocini del Prof. Carles Simó, a l’autor o autors d’un article a l’àrea de Sistemes Dinàmics, publicat entre l’1 de febrer de 2019 i el 31 de gener de 2023.
Premiats:
Els premiats han estat Massimiliano Berti, Alberto Maspero i Paolo Ventura, autors de l’article “Full description of Benjamin-Feir instability of Stokes waves in deep water“, Invent. Math.
230 (2022), no. 2, 651–711.
El jurat, format per Vadim Kaloshin, Maria Jose Pacifico, Susanna Terracini, Dmitry Treschev i Amie Wilkinson, amb Amadeu Delshams (UPC) ocm a secretari ha destacat el valor del seu treball.
A problem of fundamental importance in fluid mechanics is the stability/instability of traveling periodic Stokes waves. In 1967 Benjamin and Feir proposed a famous heuristic mechanism which leads to the disintegration of the wave train subject to long wave perturbations.
After more than 50 years, this paper by M. Berti, A. Maspero and P. Ventura provides, in a mathematically rigorous way, the complete splitting of the four eigenvalues close to zero of the linearized water waves equations at a Stokes solution of small amplitude, as the Floquet exponent is turned. This proves the long standing conjecture that as the Floquet exponent varies, the pair of non-purely imaginary eigenvalues traces out a closed figure eight. The proof of this breakthrough result deeply exploits the Hamiltonian and reversible nature of the water waves equations and merges, in an unconventional way, different spectral and dynamical systems techniques.
Agraim al jurat al seva dedicació i l’esforç per prendre la decisió, tenint en compte l’alta qualitat dels treballs presentats a aquest premi.
