Work

Norm inflation for the derivative nonlinear Schrödinger equation

Year: 2024

Type: article

Abstract: In this note, we study the ill-posedness problem for the derivative nonlinear Schrödinger equation (DNLS) in the one-dimensional setting. More precisely, by using a ternary-quinary tree expansion of the Duhamel formula we prove norm inflation in Sobolev spaces below the (scaling) critical regularity for the gauged DNLS. This ill-posedness result is sharp since DNLS is known to be globally well-posed in L 2 ( ℝ ) [16]. The main novelty of our approach is to control the derivative loss from the cubic nonlinearity by the quintic nonlinearity with carefully chosen initial data.

Source: Comptes Rendus Mathématique

DOI: 10.5802/crmath.566

Authors: Yuzhao Wang, Younes Zine

Language: English

Topic: Advanced Mathematical Physics Problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: Engineering and Physical Sciences Research Council, H2020 European Research Council

Awards: Dynamics of singular stochastic nonlinear dispersive PDEs, G6472360097, Singular Stochastic Dispersive Dynamics

OpenAlex ID: W4404964897

FWCI: 0.651

Cites: 30

Cited by: 1

Related to: 10