• 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
• 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…
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## References

SHOWING 1-10 OF 79 REFERENCES
Maximum amplification of enstrophy in three-dimensional Navier–Stokes flows
• Mathematics, Physics
Journal of Fluid Mechanics
• 2020
This investigation concerns a systematic search for potentially singular behaviour in three-dimensional (3-D) Navier–Stokes flows. Enstrophy serves as a convenient indicator of the regularity of
Numerical investigations of non-uniqueness for the Navier-Stokes initial value problem in borderline spaces
• Mathematics, Physics
• 2017
We consider the Cauchy problem for the incompressible Navier-Stokes equations in $\mathbb{R}^3$ for a one-parameter family of explicit scale-invariant axi-symmetric initial data, which is smooth away
Quantitative bounds for critically bounded solutions to the Navier-Stokes equations
We revisit the regularity theory of Escauriaza, Seregin, and Sverak for solutions to the three-dimensional Navier-Stokes equations which are uniformly bounded in the critical $L^3_x(\mathbf{R}^3)$
Late formation of singularities in solutions to the Navier?Stokes equations
We study how late the first singularity can form in solutions of the Navier?Stokes equations and estimate the size of the potentially dangerous time interval, where it can possibly appear. According
A local smoothness criterion for solutions of the 3D Navier-Stokes equations
• Mathematics
• 2014
We consider the three-dimensional Navier–Stokes equations on the whole space R3 and on the three-dimensional torus T3. We give a simple proof of the local existence of (finite energy) solutions in L3
Remarks on the Navier-Stokes Equations
Necessary and sufficient conditions for the absence of singularities in solutions of the three dimensional Navier-Stokes equations are recalled. New global weak solutions are constructed. They enjoy
On maximum enstrophy growth in a hydrodynamic system
• Mathematics
• 2011
Abstract Enstrophy E plays an important role in the study of regularity of solutions to the three-dimensional Navier–Stokes equation. The best estimates for its growth available to-date do not rule
Solutions for semilinear parabolic equations in Lp and regularity of weak solutions of the Navier-Stokes system
Abstract We construct a unique local regular solution in L q (0, T ; L p ) for a class of semilinear parabolic equations which includes the semilinear heat equation u t − Δu = ¦u¦ α u (α > 0) and the
Lower bounds on blow up solutions of the three-dimensional Navier–Stokes equations in homogeneous Sobolev spaces
• Mathematics
• 2012
Suppose that u(t) is a solution of the three-dimensional Navier–Stokes equations, either on the whole space or with periodic boundary conditions, that has a singularity at time T. In this paper we
Potentially singular solutions of the 3D axisymmetric Euler equations
• Physics, Medicine
Proceedings of the National Academy of Sciences
• 2014
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.