论文标题
改善了三层甲板和相关模型的良好适合度
Improved well-posedness for the Triple-Deck and related models via concavity
论文作者
论文摘要
我们在gevrey中建立了三甲板系统的线性化良好性 - $ \ frac32 $在切向变量中的规律性，在背景流对凹度假设下。由于最近的结果\ cite {dietertgv}，人们不能期望\ cite {iyervicol}的结果对定期类别\ cut {iyervicol}的结果比实际的分析性较弱。我们的方法通过分析傅立叶宽面的时空模式来利用两种成分：i）在涡度水平上的稳定性估计，涉及凹度假设和一个微妙的迭代方案，从\ cite {gvmm} ii）适用于Benjamin-ono-ono-ono-ono-ono one equartion from the flow flow flow flow flow flow flow flow flow。有趣的是，我们对涡度方程的处理也适应了所谓的静水液压Navier-Stokes方程：我们为该系统显示出类似的Gevrey-$ \ frac32 $线性良好的凹入结果，用于凹入数据，在线性级别上改善了线性级别的工作\ CITE {MR4149066}。
We establish linearized well-posedness of the Triple-Deck system in Gevrey-$\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}.
