Blow up for nonlinear wave-type equations with perturbed derivatives

2025/08/11 by Felisia Angela Chiarello, G. Girardi, Chiarello, F. A. +3
Engineering · Mathematics · Physics and Astronomy · #35B33 #35L70 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Waves and Solitons #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2508.08089

openalex publication_date 2025/08/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate semilinear wave-type equations that can be recast as wave equations with derivatives perturbed by zero-order terms. This framework covers several well-studied cases, including the scale-invariant wave equation. In this setting, we refine existing blow-up results for radial initial data with suitable decay, and identify conditions on the zero-order terms that govern the interplay between derivative perturbations, initial data size, and nonlinearity exponent.

Citations

• Critical exponent for nonlinear damped wave equations with non-negative potential in 3D
• On large potential perturbations of the Schrödinger, wave and Klein--Gordon equations
• Magnetic virial identities, weak dispersion and Strichartz inequalities
• Strichartz and smoothing estimates for dispersive equations with magnetic potentials
• Weighted Strichartz estimates and global existence for semilinear wave equations
• Normal forms and quadratic nonlinear Klein‐Gordon equations

Related

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• Blow-up behavior for the Klein-Gordon and other perturbed semilinear wave equations