Note on Prodi-Serrin-Ladyzhenskaya type regularity criteria for the Navier-Stokes equations

Chuong Van Tran; Xinwei Yu

doi:10.1063/1.4974020

Note on Prodi-Serrin-Ladyzhenskaya type regularity criteria for the Navier-Stokes equations

Chuong Van Tran, Xinwei Yu

Applied Mathematics

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Abstract

In this article we prove new regularity criteria of the Prodi-Serrin-Ladyzhenskaya type for the Cauchy problem of the three-dimensional incompressible Navier-Stokes equations. Our results improve the classical L^r(0,T;L^s) regularity criteria for both velocity and pressure by factors of certain nagative powers of the scaling invariant norms ||u||_L³ and ||u||_H^1/2.

Original language	English
Article number	011501
Number of pages	10
Journal	Journal of Mathematical Physics
Volume	58
Issue number	1
DOIs	https://doi.org/10.1063/1.4974020
Publication status	Published - 18 Jan 2017

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© 2017, the Author(s). This work has been made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1063/1.4974020
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title = "Note on Prodi-Serrin-Ladyzhenskaya type regularity criteria for the Navier-Stokes equations",

abstract = "In this article we prove new regularity criteria of the Prodi-Serrin-Ladyzhenskaya type for the Cauchy problem of the three-dimensional incompressible Navier-Stokes equations. Our results improve the classical Lr(0,T;Ls) regularity criteria for both velocity and pressure by factors of certain nagative powers of the scaling invariant norms ||u||L3 and ||u||H1/2.",

author = "Tran, {Chuong Van} and Xinwei Yu",

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AU - Yu, Xinwei

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N2 - In this article we prove new regularity criteria of the Prodi-Serrin-Ladyzhenskaya type for the Cauchy problem of the three-dimensional incompressible Navier-Stokes equations. Our results improve the classical Lr(0,T;Ls) regularity criteria for both velocity and pressure by factors of certain nagative powers of the scaling invariant norms ||u||L3 and ||u||H1/2.

AB - In this article we prove new regularity criteria of the Prodi-Serrin-Ladyzhenskaya type for the Cauchy problem of the three-dimensional incompressible Navier-Stokes equations. Our results improve the classical Lr(0,T;Ls) regularity criteria for both velocity and pressure by factors of certain nagative powers of the scaling invariant norms ||u||L3 and ||u||H1/2.

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Note on Prodi-Serrin-Ladyzhenskaya type regularity criteria for the Navier-Stokes equations

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