Blowup for the fractional KGS system with nongauge nonlinearities

Jun Pu; Qihong Shi; Jun Pu; Qihong Shi

doi:10.3934/era.2026008

Electronic Research Archive

2026, Volume 34, Issue 1: 160-172. doi: 10.3934/era.2026008

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Research article

Blowup for the fractional KGS system with nongauge nonlinearities

Jun Pu ^1,2,
Qihong Shi ^{1
,
,}

1.
Department of Mathematics, Lanzhou University of Technology, Lanzhou 730050, China
2.
Gansu Earthquake Agency, Lanzhou 730000, China

Received: 17 July 2025 Revised: 14 November 2025 Accepted: 25 November 2025 Published: 05 January 2026

In this paper, we investigate the finite-time blowup phenomenon in the fractional Klein-Gordon-Schrödinger (FKGS) system featuring nongauge-invariant power-type nonlinearities on $ \mathbb{R}^{n} $. The system models interactions between nucleon and meson fields, augmented by fractional Laplacian operators and nonlinear terms that disrupt conservation laws. By introducing a novel test function tailored to address the difficulties posed by mixed fractional operators and the absence of energy conservation, we established sufficient conditions for finite-time blowup under specific initial data constraints. Our analysis revealed that solutions fail to exist globally when the nonlinear exponents and initial energy satisfy critical inequalities, with the lifespan bounded by a power-law dependence on the problem parameters.
- FKGS system,
- test function,
- weak solution,
- blowup
Citation: Jun Pu, Qihong Shi. Blowup for the fractional KGS system with nongauge nonlinearities[J]. Electronic Research Archive, 2026, 34(1): 160-172. doi: 10.3934/era.2026008

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Abstract

In this paper, we investigate the finite-time blowup phenomenon in the fractional Klein-Gordon-Schrödinger (FKGS) system featuring nongauge-invariant power-type nonlinearities on $ \mathbb{R}^{n} $. The system models interactions between nucleon and meson fields, augmented by fractional Laplacian operators and nonlinear terms that disrupt conservation laws. By introducing a novel test function tailored to address the difficulties posed by mixed fractional operators and the absence of energy conservation, we established sufficient conditions for finite-time blowup under specific initial data constraints. Our analysis revealed that solutions fail to exist globally when the nonlinear exponents and initial energy satisfy critical inequalities, with the lifespan bounded by a power-law dependence on the problem parameters.

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