• Corpus ID: 238634273

Searching for Singularities in Navier-Stokes Flows Based on the Ladyzhenskaya-Prodi-Serrin Conditions

@inproceedings{Kang2021SearchingFS,
  title={Searching for Singularities in Navier-Stokes Flows Based on the Ladyzhenskaya-Prodi-Serrin Conditions},
  author={Di Kang and Bartosz Protas},
  year={2021}
}
  • Di Kang, B. Protas
  • Published 11 October 2021
  • Mathematics, Physics
In this investigation we perform a systematic computational search for potential singularities in 3D Navier-Stokes flows based on the Ladyzhenskaya-Prodi-Serrin conditions. They assert that if the quantity ∫ T 0 ‖u(t)‖pLq(Ω) dt, where 2/p+ 3/q ≤ 1, q > 3, is bounded, then the solution u(t) of the Navier-Stokes system is smooth on the interval [0, T ]. In other words, if a singularity should occur at some time t ∈ [0, T ], then this quantity must be unbounded. We have probed this condition by… 
Systematic Search For Extreme and Singular Behavior in Some Fundamental Models of Fluid Mechanics
This review article offers a survey of the research program focused on a systematic computational search for extreme and potentially singular behavior in hydrodynamic models motivated by open

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TLDR
This paper attempts to provide an affirmative answer to this long-standing open question from a numerical point of view, by describing a class of rotationally symmetric flows from which infinitely fast spinning vortices can form in finite time.
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