Wild solutions of the Navier–Stokes equations whose singular sets in time have Hausdorff dimension strictly less than 1
By T. Buckmaster, Maria Colombo, Vlad Vicol. Journal of the European Mathematical Society (Print), 2018
135 citations recorded by the source corpus.
We prove non-uniqueness for a class of weak solutions to the Navier-Stokes equations which have bounded kinetic energy, integrable vorticity, and are smooth outside a fractal set of singular times with Hausdorff dimension strictly less than 1.
Subfields: Applied Mathematics, Computational Mechanics
View Paper: https://www.semanticscholar.org/paper/b9dd240b6607e7730c07e5b27ad1ed1095196bf4
How researchers see this paper
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In Applied Mathematics
- Xiangchan Zhu
- Rongchan Zhu
- Martina Hofmanov'a
- Maria Colombo
- Elia Brué
- Dallas Albritton
- Vlad Vicol
- T. Buckmaster
In Computational Mechanics
- Maria Colombo
- Xiangchan Zhu
- Rongchan Zhu
- Martina Hofmanov'a
- Elia Brué
- Vlad Vicol
- Dallas Albritton
- T. Buckmaster
Citations in the corpus
- Non-uniqueness of Leray solutions of the forced Navier-Stokes equations (2021, methodology): “Buckmaster and Vicol [12] (see also [8]) demonstrated nonuniqueness of distributional solutions to the Cauchy problem for the Navier-Stokes equations via the convex integration method for any L(2) initial datum.”
- On Ill‐ and Well‐Posedness of Dissipative Martingale Solutions to Stochastic 3D Euler Equations (2020, methodology): “The method was then further developed and successfully applied to a number of other fluid dynamics models, in particular to the Navier–Stokes system in three dimensions by Buckmaster and Vicol [14] and Buckmaster, Colombo, and Vicol [12], which permitted proving nonuniqueness for weak solutions not ”
- Global-in-time probabilistically strong and Markov solutions to stochastic 3D Navier–Stokes equations: Existence and nonuniqueness (2021, methodology): “But actually already the seminal paper by Buckmaster and Vicol [BV19b] provides the necessary nonuniqueness result of weak solutions with a prescribed energy.”
- Convex integration and phenomenologies in turbulence (2019, methodology): “For the intermittent jets of [15] we have”