Inviscid dynamical structures near Couette flow

Details Inviscid dynamical structures near Couette flow Inviscid dynamical structures near Couette flow

2010-04-28

arxiv.org/abs/1004.5149v1

Mathematics

Analysis of PDEs

Scientific paper

Consider inviscid fluids in a channel {-1(3/2)) neighborhood of Couette, we show that there exist no non-parallel steadily travelling flows v(x-ct,y), and no unstable shears. This suggests that the long time dynamics in H^{s}(s>(3/2)) neighborhoods of Couette might be much simpler. Such contrasting dynamics in H^{s} spaces with the critical power s=(3/2) is a truly nonlinear phenomena, since the linear inviscid damping near Couette is true for any initial vorticity in L^2.

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