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

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...

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Published inPhysica. D Vol. 237; no. 10; pp. 1346 - 1351
Main Author Marchand, Fabien
Format Journal Article
LanguageEnglish
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
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Abstract 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 ) .
AbstractList 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 ) .
Author Marchand, Fabien
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Keywords 92.10.-c
Weak solutions
Uniqueness
Critical dissipation
47.10.ad
The 2D quasi-geostrophic equation
47.90.+a
92.60.-e
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Snippet 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 ̇ −...
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SubjectTerms Critical dissipation
The 2D quasi-geostrophic equation
Uniqueness
Weak solutions
Title Weak–strong uniqueness criteria for the critical quasi-geostrophic equation
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