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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Systematic Search For Singularities in 3D Navier-Stokes Flows

## Systematic Search For Singularities in 3D Navier-Stokes FlowsAdd to your list(s) Download to your calendar using vCal - Bartosz Protas (McMaster University)
- Monday 07 March 2022, 13:30-14:30
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact nobody. TURW03 - Modelling and analysis of turbulent transport, mixing and scaling This investigation concerns a systematic computational search for potentially singular behavior in 3D Navier-Stokes flows. Enstrophy $\mathcal{E}(t)$ serves as a convenient indicator of the regularity of solutions to the Navier Stokes equation—- as long as this quantity remains finite, the solutions are guaranteed to be smooth and satisfy the equations in the classical (pointwise) sense. Another well-known conditional regularity result are the Ladyzhenskaya-Prodi-Serrin conditions asserting that the quantity $\mathcal{L} $, we consider families of PDE optimization problems in which initial conditions are sought subject to certain constraints so that these quantities in the resulting Navier-Stokes flows are maximized. These problems are solved computationally using a large-scale adjoint-based gradient approach. By solving these problems for a broad range of parameter values we demonstrate that the maximum growth of $\mathcal{E}(T)$ and $\mathcal{L}{q,p}$ appears finite and follows well-defined power-law relations in terms of the size of the initial data. Thus, in the worst-case scenarios the two quantities remain bounded for all times and there is no evidence for singularity formation in finite time. We will also review earlier results where a similar approach allowed us to probe the sharpness of a priori bounds on the growth of enstrophy and palinstrophy in 1D Burgers and 2D Navier-Stokes flows.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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