Work

Large Amplitude Quasi-Periodic Traveling Waves in Two Dimensional Forced Rotating Fluids

Year: 2025

Type: article

Abstract: with a large quasi-periodic traveling wave external force. These solutions exhibit large sizes, which depend on the frequency of oscillations of the external force. Due to the presence of small divisors, the proof relies on a nonlinear Nash-Moser scheme tailored to construct nonlinear waves of large size. To our knowledge, this is the first instance of constructing quasi-periodic solutions for a quasilinear PDE in dimensions greater than one, with a 1-smoothing dispersion relation that is highly degenerate - indicating an infinite-dimensional kernel for the linear principal operator. This degeneracy challenge is overcome by preserving the traveling-wave structure, the conservation of momentum and by implementing normal form methods for the linearized system with sublinear dispersion relation in higher space dimension.

Source: Communications in Mathematical Physics

DOI: 10.1007/s00220-025-05247-z

Authors: Roberta Bianchini, Luca Franzoi, Riccardo Montalto, Shulamit Terracina

Institutions: National Research Council, University of Milan, Scuola Internazionale Superiore di Studi Avanzati

Language: English

Topic: Advanced Mathematical Physics Problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,990

Funders: Università degli Studi di Milano, European Research Council