Regularity Criteria for Weak Solutions to the Navier–Stokes Equations in Terms of Spectral Projections of Vorticity and Velocity

Jiří Neustupa; Patrick Penel; Minsuk Yang

doi:10.1007/s00021-022-00728-w

Regularity Criteria for Weak Solutions to the Navier–Stokes Equations in Terms of Spectral Projections of Vorticity and Velocity

Jiří Neustupa, Patrick Penel, Minsuk Yang

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

We deal with a weak solution v to the Navier–Stokes initial value problem in R³× (0 , T) , that satisfies the strong energy inequality. We impose conditions on certain spectral projections of ω:=curlv or just v, and we prove the regularity of solution v. The spectral projection is defined by means of the spectral resolution of identity associated with the self–adjoint operator curl.

Original language	English
Article number	104
Journal	Journal of Mathematical Fluid Mechanics
Volume	24
Issue number	4
DOIs	https://doi.org/10.1007/s00021-022-00728-w
Publication status	Published - 2022 Nov

Bibliographical note

Funding Information:
The first author has been supported by the Grant Agency of the Czech Republic, grant No. 22-01591S, and the Academy of Sciences of the Czech Republic (RVO 67985840). The third author has been supported by the National Research Foundation of Korea (NRF), grant No. 2021R1A2C4002840.

Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

All Science Journal Classification (ASJC) codes

Mathematical Physics
Condensed Matter Physics
Computational Mathematics
Applied Mathematics

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abstract = "We deal with a weak solution v to the Navier–Stokes initial value problem in R3× (0 , T) , that satisfies the strong energy inequality. We impose conditions on certain spectral projections of ω:=curlv or just v, and we prove the regularity of solution v. The spectral projection is defined by means of the spectral resolution of identity associated with the self–adjoint operator curl.",

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T1 - Regularity Criteria for Weak Solutions to the Navier–Stokes Equations in Terms of Spectral Projections of Vorticity and Velocity

AU - Neustupa, Jiří

AU - Penel, Patrick

AU - Yang, Minsuk

N1 - Funding Information: The first author has been supported by the Grant Agency of the Czech Republic, grant No. 22-01591S, and the Academy of Sciences of the Czech Republic (RVO 67985840). The third author has been supported by the National Research Foundation of Korea (NRF), grant No. 2021R1A2C4002840. Publisher Copyright: © 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

PY - 2022/11

Y1 - 2022/11

N2 - We deal with a weak solution v to the Navier–Stokes initial value problem in R3× (0 , T) , that satisfies the strong energy inequality. We impose conditions on certain spectral projections of ω:=curlv or just v, and we prove the regularity of solution v. The spectral projection is defined by means of the spectral resolution of identity associated with the self–adjoint operator curl.

AB - We deal with a weak solution v to the Navier–Stokes initial value problem in R3× (0 , T) , that satisfies the strong energy inequality. We impose conditions on certain spectral projections of ω:=curlv or just v, and we prove the regularity of solution v. The spectral projection is defined by means of the spectral resolution of identity associated with the self–adjoint operator curl.

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ER -

Regularity Criteria for Weak Solutions to the Navier–Stokes Equations in Terms of Spectral Projections of Vorticity and Velocity

Abstract

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