Partial regularity of Solutions of Navier-Stokes equations
By Xixia Ma. 2016
124 citations recorded by the source corpus.
In this paper, we study the singular set of 3-dimensional Navier-Stokes equations. Under the condition$\frac{1}{R^{\frac{3s}{q}+2-s}}\int^{R^{2}}_{0}(\int_{B_{R}}|u|^{q}dx)^{\frac{s}{q}}ds <C,$ for $(q,s)\in\{(2,5),(5,2)\},$ we use the backward uniqueness of parabolic equations to show that the Hausdorff dimension of the singular set is less than 1.
Subfields: Applied Mathematics, Control and Systems Engineering
View Paper: https://www.semanticscholar.org/paper/1cd18da40176f7c2d5045ec2baf04f5c96e341dd
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In Applied Mathematics
- Maria Colombo
- Vlad Vicol
- T. Buckmaster
- Martina Hofmanov'a
- Patrick Winkert
- Xiangchan Zhu
- Rongchan Zhu
- Elia Brué
In Control and Systems Engineering
Citations in the corpus
- Wild solutions of the Navier–Stokes equations whose singular sets in time have Hausdorff dimension strictly less than 1 (2018, methodology): “[42] V. Scheffer.”
- Nonuniqueness of weak solutions to the Navier-Stokes equation (2017, unknown): “Based on the natural scaling of the equations v(x, t) 7→ vλ(x, t) = λv(λx, λ2t), a number of partial regularity results have been established [46, 7, 41, 37, 54, 35]; the local existence for the Cauchy problem has been proven in scaling-invariant spaces [30, 32, 28]; and conditional regularity has b”
- Convex integration and phenomenologies in turbulence (2019, methodology): “In the seminal work [173], Scheffer demonstrated the existence of non-trivial weak solutions with compact support in time (cf. [178, 179]).”