Equality of computable solutions and DMV solutions

Determine whether the set of computable solutions \mathcal{U}_{\rm comp}[_0, v_0, S_0, \mathcal{E}_0]—defined as strong limits of Cesàro averages of sequences of consistent approximations—equals the full DMV solution set \mathcal{U}[_0, v_0, S_0, \mathcal{E}_0], at least for some specific classes of initial data.

Background

The authors introduce a restricted, ‘computable’ class built from empirical averages of consistent approximations, which is nonempty, closed, and convex, and contains all weak solutions.

They ask whether this computable class exhausts all DMV solutions, which would align admissible solutions with numerically realizable limits and potentially simplify selection procedures.

References

Open problem VII: We have \mathcal{U}{\rm comp}[_0, v_0, S_0, \mathcal{E}_0] \subset \mathcal{U}[_0, v_0, S_0, \mathcal{E}_0]. Is it true that \mathcal{U}{\rm comp}[_0, v_0, S_0, \mathcal{E}_0] = \mathcal{U}[_0, v_0, S_0, \mathcal{E}_0] at least for a specific class of initial data?

— The Euler system of gas dynamics  (2603.29619 - Feireisl, 31 Mar 2026) in Section 4.4, “Reducing the set of eligible DMV solutions, computable solutions”