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We consider the Yang-Mills problem on $\mathbb{R}^{1+4}$ with gauge group$SO(4)$. In an appropriate equivariant reduction, this Yang-Mills problemreduces to a single scalar semilinear wave equation. This semilinear equationadmits a one-parameter family of solitons, each of which is a re-scaling of afixed solution. In this work, we construct a class of solutions, each of whichconsists of a soliton whose length scale is asymptotically constant, coupled tolarge radiation, plus corrections which slowly decay to zero in the energynorm. Our class of solutions includes ones for which the radiation component isonly "logarithmically" better than energy class. As such, the solutions are notconstructed by apriori assuming the length scale to be constant. Instead, weuse an approach similar to a previous work of the author regarding wave maps.In the setup of this work, the soliton length scale asymptoting to a constantis a necessary condition for the radiation profile to have finite energy. Aninteresting point of our construction is that, for each radiation profile,there exist one-parameter families of solutions consisting of the radiationprofile coupled to a soliton, which has any asymptotic value of the lengthscale.

Global, Non-Scattering Solutions to the Energy Critical Yang-Mills Problem