Blow-up results for the semilinear Schrödinger equations with forcing and gradient terms: the critical cases

Torebek B.T.
August 2025 Birkhauser

Zeitschrift fur Angewandte Mathematik und Physik
2025 #76 Issue 4

The paper is devoted to the study of critical cases of the nonlinear Schrödinger equation (NLS) with source and gradient terms, subsequently providing answers to some open questions posed by Alotaibi et al. (Z Angew Math Phys, 73:1–17, 2022). The main results state that in critical cases, the problem under consideration does not have any global-in-time weak solutions. The proof approach is based on modified method of test functions specifically adapted to the nature of the considered problem.

Blow-up , Critical exponent , Forcing term , Gradient nonlinearity , Schrödinger (NLS) equation

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Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Ghent, Belgium

Institute of Mathematics and Mathematical Modeling
Department of Mathematics: Analysis

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