Global well‐posedness and blow‐up criterion for the periodic quasi‐geostrophic equations in Lei‐Lin‐Gevrey spaces | Zendy

Benhamed Moez | Zendy

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Global well‐posedness and blow‐up criterion for the periodic quasi‐geostrophic equations in Lei‐Lin‐Gevrey spaces

Author(s) -

Benhamed Moez

Publication year - 2017

Publication title -

mathematical methods in the applied sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.719

H-Index - 65

eISSN - 1099-1476

pISSN - 0170-4214

DOI - 10.1002/mma.4543

Subject(s) - mathematics , uniqueness , geostrophic wind , mathematical analysis , initial value problem , dissipation , type (biology) , physics , mechanics , thermodynamics , ecology , biology

In this paper we consider a periodic 2‐dimensional quasi‐geostrophic equations with subcritical dissipation. We show the global existence and uniqueness of the solution θ ∈ C ( [ 0 , T ] , Y a , σ 1 − 2 α ( T 2 ) ) for small initial data in the Lei‐Lin‐Gevrey spacesY a , σ 1 − 2 α ( T 2 ) . Moreover, we establish an exponential type explosion in finite time of this solution.

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