For the Landau equation with soft potentials (including Coulomb), this paper proves that all H-solutions with enough moments coincide with the smooth solution, via a relative entropy estimate.
A Priori Estimates for Solu- tions to Landau Equation Under Prodi–Serrin Like Criteria
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Weak-strong uniqueness for the Landau equation by a relative entropy method
For the Landau equation with soft potentials (including Coulomb), this paper proves that all H-solutions with enough moments coincide with the smooth solution, via a relative entropy estimate.