Construction of two-bubble solutions for some energy-critical wave equations

Jendrej, Jacek

Séminaire Laurent Schwartz — EDP et applications (2015-2016), Exposé no. 21, 10 p.

We present a construction of pure two-bubbles for some energy-critical wave equations, that is solutions which in one time direction approach a superposition of two stationary states both centered at the origin, but asymptotically decoupled in scale. Our solution exists globally, with one bubble at a fixed scale and the other concentrating in infinite time, with an error tending to $0$ in the energy space. We treat the cases of the power nonlinearity in space dimension $6$, the radial Yang-Mills equation and the equivariant wave maps equation with equivariance class $k\ge 3$. The concentration speed of the second bubble is exponential for the first two models and a power function in the last case.

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