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

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