Work

Growth of Sobolev norms for 2d cubic NLS with partial harmonic potential

Year: 2024

Type: article

Abstract: In this paper, we study the $ 2 $D cubic nonlinear Schrödinger equation (NLS) with the partial harmonic potential. First, we prove the local well-posedness in Bourgain spaces by establishing a key bilinear estimate associated with the partial harmonic oscillator. Then, we give the polynomial bound of the Sobolev norms for the solutions using the method of the Planchon, Tzvetkov, and Visciglia in [Rev. Mat. Iberoam, 39(2023), 1405-1436].

Source: Communications on Pure &amp Applied Analysis

DOI: 10.3934/cpaa.2024090

Authors: Mingming Deng, Xiaoyan Su, Jiqiang Zheng

Institutions: Loughborough University, Institute of Applied Physics and Computational Mathematics

Language: English

Topic: Advanced Mathematical Physics Problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4403356437

FWCI: 0.65

Cites: 6

Cited by: 1

Related to: 10