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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Elementary excitations for the 3D Navier-Stokes equations

## Elementary excitations for the 3D Navier-Stokes equationsAdd to your list(s) Download to your calendar using vCal - Koji Ohkitani (Research Institute for Mathematical Sciences , Kyoto University)
- Monday 13 June 2022, 16:00-17:00
- Seminar Room 2, Newton Institute.
If you have a question about this talk, please contact nobody. TUR - Mathematical aspects of turbulence: where do we stand? We study elementary excitations for describing the late stage of decaying Navier-Stokes flows. For 2D Navier-Stokes flows it is well-known that the late stage of the time evolution is represented by the so-called Burgers vortices. Here we will seek an analogue of such elementary excitations (i.e. building blocks) for 3D Navier-Stokes flows. We begin 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 structure. We will raise and answer the following questions about solutions to the dynamically-scaled Navier-Stokes equations: Can we find functions which map the linearised solutions to the nonlinear ones ? If so, in which dependent variables can we do that ? Also addressed is the implications on the non-integrability of the Navier-Stokes equations. (Part of this work is joint with R. Vanon.) This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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