Fast rotation and inviscid limits for the SQG equation with general ill-prepared initial data

Abstract

In the present paper, we study the fast rotation and inviscid limits for the 2-D dissipative surface quasi-geostrophic equation with a dispersive forcing term $A{\mathcal{R}}_1\vartheta$, in the domain $\Omega ={\mathbb{T}}^1\times \mathbb{R}$. In the case when we perform the fast rotation limit (keeping the viscosity fixed), in the context of general ill-prepared initial data, we prove that the limit dynamics is described by a linear equation. On the other hand, performing the combined fast rotation and inviscid limits, we show that the initial data ${\overline{\vartheta }}_0$ is transported along the motion. The proof of the convergence is based on an application of the Aubin-Lions lemma.

Submitted. arXiv admin note: text overlap with arXiv:2005.04279, arXiv:2106.13699, arXiv:2109.09841, arXiv:2205.11889