Unconditional uniqueness of renormalized reaction–diffusion solutions

Prove unconditional uniqueness of renormalized solutions for deterministic reaction–diffusion systems equipped with an entropic structure, beyond the currently available weak–strong uniqueness theory.

Background

For deterministic reaction–diffusion systems with entropic structures, existing results establish global renormalized solutions irrespective of the reaction growth rate and also establish weak–strong uniqueness. Weak–strong uniqueness, however, only guarantees uniqueness when a sufficiently regular strong solution is available.

The unresolved issue is unconditional uniqueness within the full class of renormalized solutions. The paper contrasts this situation with the three-dimensional Navier–Stokes problem and does not resolve uniqueness for deterministic renormalized solutions.

References

Nevertheless, the unconditional uniqueness of renormalized solutions remains entirely open.

— Global classical solutions by transport noise for reaction-diffusion systems with entropy dissipation  (2608.13332 - Agresti et al., 13 Aug 2026) in Section 1, paragraph beginning “To bypass these difficulties”