Work

Sobolev instability in the cubic NLS equation with convolution potentials on irrational tori

Year: 2024

Type: article

Abstract: In this paper we prove the existence of solutions to the cubic NLS equation with convolution potentials on two dimensional irrational tori undergoing an arbitrarily large growth of Sobolev norms as time evolves. Our results apply also to the case of square (and rational) tori. We weaken the regularity assumptions on the convolution potentials, required in a previous work by Guardia (2014) [11] for the square case, to obtain the H s -instability ( s > 1 ) of the elliptic equilibrium u = 0 . We also provide the existence of solutions u ( t ) with arbitrarily small L 2 norm which achieve a prescribed growth, say ‖ u ( T ) ‖ H s ≥ K ‖ u ( 0 ) ‖ H s , K ≫ 1 , within a time T satisfying polynomial estimates, namely 0 < T < K c for some c > 0 .

Source: Journal of Differential Equations

DOI: 10.1016/j.jde.2024.09.044

Author: Filippo Giuliani

Institution: Politecnico di Milano

Language: English

Topic: Advanced Mathematical Physics Problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,050

Funders: Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni, Ministero dell'Istruzione e del Merito