Abstract
We prove that the linearization of the hydrostatic Euler equations at certain parallel shear flows is ill-posed. The result also extends to the hydrostatic Navier–Stokes equations with a small viscosity.
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Renardy, M. Ill-posedness of the Hydrostatic Euler and Navier–Stokes Equations. Arch Rational Mech Anal 194, 877–886 (2009). https://doi.org/10.1007/s00205-008-0207-4
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DOI: https://doi.org/10.1007/s00205-008-0207-4