Global existence of the two-dimensional QGE with sub-critical dissipation

In this paper, we study the sub-critical dissipative quasi-geostrophic equations (Sα). We prove that there exists a unique local-in-time solution for any large initial data θ0 in the space X1−2α(R2) defined by (1). Moreover, we show that (Sα) has a global solution in time if the norms of the initial...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2015-03, Vol.423 (2), p.1330-1347
Main Authors: Benameur, Jamel, Benhamed, Moez
Format: Article
Language:English
Subjects:
Blow-up criterion
Critical spaces
Existence and uniqueness
Sub-critical
Surface quasi-geostrophic equations
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Summary:In this paper, we study the sub-critical dissipative quasi-geostrophic equations (Sα). We prove that there exists a unique local-in-time solution for any large initial data θ0 in the space X1−2α(R2) defined by (1). Moreover, we show that (Sα) has a global solution in time if the norms of the initial data in X1−2α(R2) are bounded by 1/4. Also, we prove a blow-up criterion of the local-in-time solution of (Sα).
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2014.10.066