Long-time existence and resonant approximation for the quadratic nonlinear wave equation with an anisotropic harmonic trapping

Nicolas Laillet

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arXiv · 1507.01683

Long-time existence and resonant approximation for the quadratic nonlinear wave equation with an anisotropic harmonic trapping

Nicolas Laillet

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Abstract

We establish long-time existence and uniqueness for the 2D wave equation with a harmonic potential in one direction. This proof relies on a fine study of the so-called space-time resonances of the equation. Then we derive a resonant system for this equation and we prove that it is a satisfying approximation for the original equation.

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Nicolas Laillet. 2015-07-07. Long-time existence and resonant approximation for the quadratic nonlinear wave equation with an anisotropic harmonic trapping. https://arxiv.org/abs/1507.01683

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