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

Jacek Jendrej

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arXiv · 1602.06524

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

Jacek Jendrej

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Abstract

We construct 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 map equation with equivariance class k > 2. The concentrating speed of the second bubble is exponential for the first two models and a power function in the last case.

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Jacek Jendrej. 2016-02-21. Construction of two-bubble solutions for energy-critical wave equations. https://arxiv.org/abs/1602.06524

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