Radiative Uniqueness Conjecture for bubbling wave maps

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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.

References

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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