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arXiv · 2205.15829

Improved well-posedness for the Triple-Deck and related models via concavity

David Gerard-Varet·Sameer Iyer·Yasunori Maekawa
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Abstract

We establish linearized well-posedness of the Triple-Deck system in Gevrey-$\frac32$ regularity in the tangential variable, under concavity assumptions on the background flow. Due to the recent result \cite{DietertGV}, one cannot expect a generic improvement of the result of \cite{IyerVicol} to a weaker regularity class than real analyticity. Our approach exploits two ingredients, through an analysis of space-time modes on the Fourier-Laplace side: i) stability estimates at the vorticity level, that involve the concavity assumption and a subtle iterative scheme adapted from \cite{GVMM} ii) smoothing properties of the Benjamin-Ono like equation satisfied by the Triple-Deck flow at infinity. Interestingly, our treatment of the vorticity equation also adapts to the so-called hydrostatic Navier-Stokes equations: we show for this system a similar Gevrey-$\frac32$ linear well-posedness result for concave data, improving at the linear level the recent work \cite{MR4149066}.

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David Gerard-Varet, Sameer Iyer, Yasunori Maekawa. 2022-05-31. Improved well-posedness for the Triple-Deck and related models via concavity. https://doi.org/10.1007/s00021-023-00809-4

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