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Weak-strong uniqueness criteria for the critical quasi-geostrophic equation. (English) Zbl 1143.76339
Summary: We give two weak-strong uniqueness results for the weak solutions to the critical dissipative quasi-geostrophic equation when the initial data belongs to \(\dot H ^{-1/2}\). The first one shows that we can construct a unique \(\dot H ^{-1/2}\)-solution when the initial data belongs moreover to \(L^\infty \) with a small \(L^\infty \) norm. The other one gives the uniqueness of a \(\dot H ^{-1/2}\)-solution which belongs to \(\mathcal C([0,T),CMO)\).

MSC:
76-06 Proceedings, conferences, collections, etc. pertaining to fluid mechanics
00B25 Proceedings of conferences of miscellaneous specific interest
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