ON THE ILL-POSEDNESS OF THE TRIPLE DECK MODEL

We analyze the stability properties of the so-called triple deck model, a classical refinement of the Prandtl equation to describe boundary layer separation. Combining the methodol-ogy introduced in [A.-L. Dalibard et al., SIAM J. Math. Anal., 50 (2018), pp. 4203-4245], based on complex analysis tools, and stability estimates inspired from Dietert and Ge'\rard-Varet [Anal. PDE, 5 (2019), 8], we exhibit unstable linearizations of the triple deck equation. The growth rates of the corresponding unstable eigenmodes scale linearly with the tangential frequency. This shows that the recent result of Iyer and Vicol [Comm. Pure Appl. Math., 74 (2021), pp. 1641--1684] of local well-posedness for analytic data is essentially optimal.