Short wave stability for inviscid shear flow
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We consider the linear stability of inviscid shear flows. While it is well known that discontinuous velocity profiles lead to short wave instabilities and ill-posedness, known examples of instability for smooth profiles have a short wave cutoff; i.e., there is a critical wave number beyond which no unstable eigenvalues exist. This paper proves a result to this effect under suitable assumptions on the base flow profile.