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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:423

Article

Benameur, Jamel¹  Benhamed, Moez² 

[1] King Saud Univ, Dept Math, Coll Sci, Riyadh 11451, Saudi Arabia

[2] Univ Tunis El Manar, Fac Sci Tunis, Tunis 2092, Tunisia

关键词: Surface quasi-geostrophic equations;    Sub-critical;    Critical spaces;    Existence and uniqueness;    Blow-up criterion;   

DOI  :  10.1016/j.jmaa.2014.10.066

来源: Elsevier

【 摘 要 】

In this paper, we study the sub-critical dissipative quasi-geostrophic equations (S-alpha). We prove that there exists a unique local-in-time solution for any large initial data theta(0) in the space chi(1-2 alpha) (R-2) defined by (1). Moreover, we show that (S-alpha) has a global solution in time if the norms of the initial data in chi(1-2 alpha)(R-2) are bounded by 1/4. Also, we prove a blow-up criterion of the local-in-time solution of (S-alpha). (C) 2014 The Authors. Published by Elsevier Inc.

【 授权许可】

Free