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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.