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SUMMARY:Elementary excitations for the 3D Navier-Stokes equations - Koji O
 hkitani (Research Institute for Mathematical Sciences \, Kyoto University)
DTSTART:20220613T150000Z
DTEND:20220613T160000Z
UID:TALK173846@talks.cam.ac.uk
DESCRIPTION:We study elementary excitations for describing the late stage 
 of decaying Navier-Stokes flows. For 2D Navier-Stokes flows it is well-kno
 wn that the late stage of the time evolution is represented by the so-call
 ed Burgers vortices. Here we will seek an analogue of such elementary exci
 tations (i.e. building blocks) for 3D Navier-Stokes flows.\n&nbsp\;\nWe be
 gin by clarifying the two kinds of critical scale-invariance of the Navier
 -Stokes equations. We obtain the leading-order solution of the dynamically
 -scaled Navier-Stokes equations explicitly and characterise its spatial st
 ructure.\n&nbsp\;\nWe will raise and answer the following questions about 
 solutions to the dynamically-scaled Navier-Stokes equations:\nCan we find 
 functions which map the linearised solutions to the nonlinear ones ? If so
 \, in which dependent variables can we do that ?\nAlso addressed is the im
 plications on the non-integrability of the Navier-Stokes equations.\n&nbsp
 \;\n(Part of this work is joint with R. Vanon.)
LOCATION:Seminar Room 2\, Newton Institute
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