On the blow-up criterion for the quasi-geostrophic equations in homogeneous Besov spaces

In this paper, we consider the blow-up criterion for the quasi-geostrophic equations with dissipation Λγ (0<γ<1). By establishing a new trilinear estimate, we show that if θ∈Lγγ+s−1(0,T;Ḃ∞,∞s(R2))for some s∈1−γ2,1, then the solution can be extended smoothly past T. This improves and extends the corresponding results in Dong and Pavlović (2009) ([32]) and Yuan (2010).