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arXiv · 2206.09467

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

Leonardo Kosloff·Gabriele Sbaiz
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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.

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Leonardo Kosloff, Gabriele Sbaiz. 2022-06-19. Fast rotation and inviscid limits for the SQG equation with general ill-prepared initial data. https://arxiv.org/abs/2206.09467

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