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

IF 2.2 1区物理与天体物理 Q1 PHYSICS, MATHEMATICAL

Communications in Mathematical Physics Pub Date : 2025-02-20 DOI:10.1007/s00220-025-05247-z

Roberta Bianchini, Luca Franzoi, Riccardo Montalto, Shulamit Terracina

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引用次数: 0

Abstract

We establish the existence of quasi-periodic traveling wave solutions for the \(\beta \)-plane equation on \({\mathbb {T}}^2\) 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.

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来源期刊

Communications in Mathematical Physics 物理-物理：数学物理

CiteScore

4.70

自引率

8.30%

发文量

226

审稿时长

3-6 weeks

期刊介绍： The mission of Communications in Mathematical Physics is to offer a high forum for works which are motivated by the vision and the challenges of modern physics and which at the same time meet the highest mathematical standards.