A unified nonlinear estimate suppresses fluid echoes and reduces the Sobolev stability threshold for 2D Boussinesq and MHD Couette flow from 1/2 to 1/3, with a logarithmic correction for MHD.
Inviscid damping and the asymptotic stability of planar shear flows in the 2d E uler equations
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Suppression of Fluid Echoes and Sobolev Stability Threshold for 2D Dissipative Fluid Equations Around Couette Flow
A unified nonlinear estimate suppresses fluid echoes and reduces the Sobolev stability threshold for 2D Boussinesq and MHD Couette flow from 1/2 to 1/3, with a logarithmic correction for MHD.