In this paper, we consider the modified quasi-geostrophic equation ∂tθ + (u · ∇)θ + κΛ αθ = 0 u = &Lambdaα-1R ⊥θ, with κ > 0, α ∈ (0, 1] and θ0 ∈ L2(ℝ2). We remark that the extra Λα-1 is introduced in order to make the scaling invariance of this system similar to the scaling invariance of the critical quasi-geostrophic equations. In this paper, we use Besov space techniques to prove global existence and regularity of strong solutions to this system.
All Science Journal Classification (ASJC) codes
- Blow up
- Global regularity
- Nonlocal equations
- Quasi-geostrophic equations