A Localized Criterion for the Regularity of Solutions to Navier-Stokes Equations

Congming Li, Chenkai Liu, Ran Zhuo

Type: Preprint

Publication Date: 2024-01-01

Citations: 0

DOI: https://doi.org/10.2139/ssrn.4887412

Abstract

The Serrin-Prodi-Ladyzhenskaya type L s,r criteria for the regularity of solutions to the incompressible Navier-Stokes equations are fundamental in the study of the millennium problem posted by the Clay Mathematical Institute about the incompressible N-S equations.In this article, we establish some localized L s,r criteria for the regularity of solutions to the equations.In fact, we obtain some a priori estimates of solutions to the equations depend only on some local L s,r type norms.These local L s,r type norms, are small for reasonable initial value and shall remain to be small for global regular solutions.Thus, deriving the smallness or even the boundedness of the local L s,r type norms is necessary and sufficient to affirmatively answer the millennium problem.

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arXiv (Cornell University) - View - PDF

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Works Cited by This (15)

Action	Title	Year	Authors
+	Boundary regularity for the Navier-Stokes equations in a half-space	1982	Vladimir Scheffer
+	On Partial Regularity of Suitable Weak Solutions to the Three-Dimensional NavierStokes equations	1999	O. A. Ladyzhenskaya G. Serëgin
+	StrongL p -solutions of the Navier-Stokes equation inR m , with applications to weak solutions	1984	Tosio Kato
+	Un teorema di unicità per le equazioni di Navier-Stokes	1959	G. A. Prodi
+	The initial value problem for the navier-stokes equations	1966	Marvin Shinbrot Shmuel Kaniel
+	Partial regularity of suitable weak solutions of the navier‐stokes equations	1982	Luis Caffarelli Robert V. Kohn Louis Nirenberg
+ PDF Chat	Partial regularity of solutions to the Navier-Stokes equations	1976	Vladimir Scheffer
+	The initial value problem for the Navier-Stokes equations with data in Lp	1972	Eugene B. Fabes B. Frank Jones N. M. Rivière
+ PDF Chat	Hausdorff measure and the Navier-Stokes equations	1977	Vladimir Scheffer
+ PDF Chat	The Navier-Stokes equations on a bounded domain	1980	Vladimir Scheffer