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

2014/08/23 by Jamel Benameur, Benameur, Jamel, Moez Benhamed +1
Engineering · Mathematics · #35A35 #35B05 #35B40 #35Q55 #81Q20 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1408.5499

openalex publication_date 2014/08/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the sub-critical dissipative quasi-geostrophic equations (\bf S_α). We prove that there exists a unique local-in-time solution for any large initial data θ₀ in the space \bf\mathcal X^1-2α(\mathbb R²) defined by (\refec). Moreover we show that (\bf S_α) has a global solution in time if the norms of the initial data in \bf\mathcal X^1-2α(\mathbb R²) are bounded by 1/4. Also, we prove a blow-up criterion of the non global solution of (\bf S_α).

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