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Landau damping: paraproducts and Gevrey regularity
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We give a new, simpler, proof of nonlinear Landau damping on T^d in Gevrey-1/s regularity (s > 1/3) which matches the regularity requirement predicted by the formal analysis of Mouhot and Villani in the original proof of Landau damping [Acta Mathematica 2011]. Our proof combines in a novel way ideas from the original proof of Landau damping and the proof of inviscid damping in 2D Euler [arXiv:1306.5028]. As in the work on 2D Euler, we use paraproduct decompositions and controlled regularity loss to replace the Newton iteration scheme employed in the original proof. We perform time-response estimates adapted from the original proof to control the plasma echoes and couple them to energy estimates on the distribution function in the style of the work on 2D Euler.
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Stability threshold of the 2D Couette flow in Sobolev spaces
For 2D Navier-Stokes near Couette flow, H^σ vorticity perturbations of size ≤ ε Re^{-1/3} are globally stable with inviscid damping and enhanced dissipation.
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