Abstract:
The objective of the note is to prove a regularity result for weak solutions to the Navier–Stokes equations that are locally in L∞(L3,∞)L∞(L3,∞). It reads that, in a sense, the number of singular points at each time is at most finite. This note is inspired by a recent paper of H. J. Choe, J. Wolf, M. Yang.
Keywords:
suitable weak solution, singular points, local regularity up to flat part of boundary.
Citation:
G. Seregin, “A note on weak solutions to the Navier–Stokes equations that are locally in L∞(L3,∞)L∞(L3,∞)”, Algebra i Analiz, 32:3 (2020), 238–253; St. Petersburg Math. J., 32:3 (2021), 565–576
\Bibitem{Ser20}
\by G.~Seregin
\paper A note on weak solutions to the Navier--Stokes equations that are locally in $L_\infty(L^{3,\infty})$
\jour Algebra i Analiz
\yr 2020
\vol 32
\issue 3
\pages 238--253
\mathnet{http://mi.mathnet.ru/aa1707}
\transl
\jour St. Petersburg Math. J.
\yr 2021
\vol 32
\issue 3
\pages 565--576
\crossref{https://doi.org/10.1090/spmj/1662}
Linking options:
https://www.mathnet.ru/eng/aa1707
https://www.mathnet.ru/eng/aa/v32/i3/p238
This publication is cited in the following 2 articles:
Tobias Barker, “Higher integrability and the number of singular points for the Navier–Stokes equations with a scale-invariant bound”, Proc. Amer. Math. Soc. Ser. B, 11:39 (2024), 436
A. A. Shlapunov, N. Tarkhanov, “An open mapping theorem for the Navier-Stokes type equations associated with the de Rham complex over Rn”, Sib. elektron. matem. izv., 18:2 (2021), 1433–1466
Citation in format AMSBIB
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