The resolution of the 4th edition of the Barcelona Dynamical Systems Prize is now public, an international award offered by the Catalan Society of Mathematics, under the sponsorship of Prof. Carles Simó, to the author or authors of an article in the area of Dynamical Systems, published between February 1, 2019 and January 31, 2023.
Awardees:
The awardees have been Massimiliano Berti, Alberto Maspero and Paolo Ventura, authors of the article «Full description of Benjamin-Feir instability of Stokes waves in deep water«, Invent. Math. 230 (2022), no. 2, 651–711.
The jury, composed of Vadim Kaloshin, Maria Jose Pacifico, Susanna Terracini, Dmitry Treschev, and Amie Wilkinson, with Amadeu Delshams (UPC) as secretary, has highlighted the value of their work.
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.
We thank the jury for their dedication and effort in making the decision, taking into account the high quality of the works submitted to this prize.
Awardees:
Massimiliano Berti
Alberto Maspero
Paolo Ventura