Radiative Uniqueness Conjecture for bubbling wave maps

Let uc(t)\boldsymbol{u}_c(t) denote the constructed blow-up solution from Part (a) of Theorem~, and let u(t)H1\boldsymbol{u}(t) \in \mathcal{H}_1 be any other solution that blows up backwards-in-time at t=0t=0 with the same radiation field u0\boldsymbol{u}^*_0. Radiative Uniqueness Conjecture. The two solutions are equal:

u(t)=uc(t).\boldsymbol{u}(t)=\boldsymbol{u}_c(t).

The conjecture would imply unique continuation of blow-up wave maps past the singularity while preserving the energy and the topological class of the solution. The source provides no resolution, so the conjecture remains open.

Sources & referencesView supporting material

Primary source

Jacek Jendrej, Andrew Lawrie and Casey Rodriguez, “Dynamics of Bubbling Wave Maps with Prescribed Radiation”, arXiv:1908.08512 (2019).

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