A 2D inhomogeneous Navier-Stokes Leray-Hopf solution becomes immediately regular exactly when it satisfies the strong energy inequality, when Danchin's weighted derivative estimates hold, and when an associated BMO-regular pressure exists; the equivalence yields weak-strong uniqueness.
Density-dependent indecompressible viscous fluids in critical spaces
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Regularity aspects of Leray-Hopf solutions to the 2D Inhomogeneous Navier-Stokes system and applications to weak-strong uniqueness
A 2D inhomogeneous Navier-Stokes Leray-Hopf solution becomes immediately regular exactly when it satisfies the strong energy inequality, when Danchin's weighted derivative estimates hold, and when an associated BMO-regular pressure exists; the equivalence yields weak-strong uniqueness.