arXiv subjects

Mingming Deng

Publications and source records attributed to Mingming Deng.

2 recordsLinked to original sources

arXiv2023

Growth of Sobolev norms for 2D cubic nonlinear Schr\"odinger equation with partial harmonic potential

In this paper, we study the $2$D cubic nonlinear Schr\"odinger 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.

math.AP↗

arXiv2023

On the growth of high Sobolev norms of the cubic nonlinear Schr\"odinger equation on $\mathbb{R}\times \mathbb{T}$

We consider the cubic nonlinear Schr\"odinger equation on product manifolds $\mathbb{R}\times \mathbb{T}$. In this paper, we obtain polynomial bounds on the growth in time of high Sobolev norms of the solutions. The main ingredient of the proof is to establish an iteration bound, which is based on the idea used by Bourgain in \cite{B1}.

math.AP↗