Year: 2026
Type: article
Abstract: We study a generalized derivative nonlinear Schrödinger equation on a bounded interval under homogeneous Dirichlet boundary conditions. Starting from the local $ H^2 $ well-posedness theory, we derive a quantitative $ H^2 $ energy inequality in physical space. The estimate yields a genuine continuation criterion at a finite endpoint, divergence of the controlling $ W^{1, \infty} $ time integral whenever the maximal time is finite, the $ H^2 $ blow-up alternative, a quantitative lower blow-up rate, and an explicit lower bound for the lifespan in terms of the initial $ H^2 $ norm. The key mechanism is a derivative-loss cancellation in the highest-order transport term. Thus, the local existence theory is supplemented by explicit maximal-time information and computable growth scales.
Source: AIMS Mathematics
Authors: Senyue Luo, Meilan Qiu, Zhiming Tan
Institutions: Guangdong Open University, Huizhou University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,200
Funder: China Scholarship Council
OpenAlex ID: W7204759286