Weak–strong uniqueness criteria for the critical quasi-geostrophic equation

• Published in: Physica. D Vol. 237; no. 10; pp. 1346 - 1351
• Main Author: Marchand, Fabien
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 15.07.2008
• Subjects: Critical dissipation; The 2D quasi-geostrophic equation; Uniqueness; Weak solutions; 92.10.-c; Weak solutions; Uniqueness; Critical dissipation; 47.10.ad; The 2D quasi-geostrophic equation; 47.90.+a; 92.60.-e
• ISSN: 0167-2789; 1872-8022
• DOI: 10.1016/j.physd.2008.03.011

We give two weak–strong uniqueness results for the weak solutions to the critical dissipative quasi-geostrophic equation when the initial data belongs to H ̇ − 1 / 2 . The first one shows that we can construct a unique H ̇ − 1 / 2 -solution when the initial data belongs moreover to L ∞ with a small L ∞ norm. The other one gives the uniqueness of a H ̇ − 1 / 2 -solution which belongs to C ( [ 0 , T ) , CMO ) .