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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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