Abstract
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 of the surface quasi-geostrophic equation with the force satisfies the growth condition in the critical BMO space , it is proved that every perturbed weak solution converges asymptotically to solution of the original surface quasi-geostrophic equation. The initial and external forcing perturbations are allowed to be large.
Highlights
Introduction and Main ResultsMathematical models in fluid dynamics play an important role in theoretical and computational studies in meteorological and oceanographic sciences and petroleum industries, and so forth
Our results show that the weak solutions θ(x, t) of the perturbed equation (4) do not need to satisfy the energy-type inequality (6) and they do not have to be regular
Together with (37) we derive the desired average decay of the difference w = θ − θ between the global solution θ of the original quasi-geostrophic equation (1) and the weak solution θ of the perturbed quasi-geostrophic equation (4): lim t→∞
Summary
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 θ(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
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