Stability Analysis of the Supercritical Surface Quasi-Geostrophic Equation

Abstract EN

This paper is devoted to the study of the stability issue of the supercritical dissipative surface quasi-geostrophic equation with nondecay low-regular external force.

Supposing that the weak solution θ(x,t) of the surface quasi-geostrophic equation with the force f∈L2(0,T;H-α/2(ℝ2)) satisfies the growth condition in the critical BMO space ∇θ∈L1(0,∞;BMO), it is proved that every perturbed weak solution θ̅(t) converges asymptotically to solution θ(t) of the original surface quasi-geostrophic equation.

The initial and external forcing perturbations are allowed to be large.