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arXiv · 2509.13188

Global existence and decay of small solutions in a viscous half Klein-Gordon equation

Louis Garénaux·Björn de Rijk
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Abstract

We establish global existence and decay of solutions of a viscous half Klein-Gordon equation with a quadratic nonlinearity considering initial data, whose Fourier transform is small in L1 cap Linfty. Our analysis relies on the observation that nonresonant dispersive effects yield a transformation of the quadratic nonlinearity into a subcritical nonlocal quartic one, which can be controlled by the linear diffusive dynamics through a standard L1 - Linfty argument. This transformation can be realized by applying the normal form method of Shatah or, equivalently, through integration by parts in time in the associated Duhamel formula.

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Louis Garénaux, Björn de Rijk. 2025-09-16. Global existence and decay of small solutions in a viscous half Klein-Gordon equation. https://arxiv.org/abs/2509.13188

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