Regularity criteria for the three-dimensional Navier-Stokes equations

2008/01/01 by Chongsheng Cao, Edriss S. Titi · 4 citations
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · doi:10.1512/iumj.2008.57.3719

crossref issued 2008/01/01 · crossref published 2008/01/01 · crossref published-print 2008/01/01 · openalex publication_date 2008/01/01 · crossref created 2008/12/22 · crossref deposited 2011/08/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/14 · crossref indexed 2026/08/01

Abstract

In this paper we consider the three-dimensional Navier-Stokes equations subject to periodic boundary condi- tions or in the whole space. We provide suYcient conditions, in terms of one component of the velocity field, or alternatively in terms of one component of the pressure gradient, for the regularity of strong solutions to the three-dimensional Navier- Stokes equations.

Citations

• StrongL p -solutions of the Navier-Stokes equation inR m , with applications to weak solutions
• L 3,∞ -solutions of the Navier-Stokes equations and backward uniqueness
• Pressure Regularity Criterion for the Three-dimensional Navier-Stokes Equations in Infinite Channel

Cited by

• On the Serrin-type condition on one velocity component for the Navier-Stokes equations
• Global Regularity vs. Finite-Time Singularities: Some Paradigms on the Effect of Boundary Conditions and Certain Perturbations
• On the local well-posedness and a Prodi-Serrin type regularity criterion of the three-dimensional MHD-Boussinesq system without thermal diffusion
• Scaling invariant Serrin criterion via one velocity component for the Navier-Stokes equations

Related

• Regularity Criteria For Strong Solutions To The 3D Navier-Stokes Equations
• The regularity criterion for 3D Navier-Stokes Equations
• Pressure Regularity Criterion for the Three-dimensional Navier-Stokes Equations in Infinite Channel
• Global regularity of the Navier-Stokes equation on thin three dimensional domains with periodic boundary conditions
• Regularity Criterion for Solutions of Three-Dimensional Turbulent Channel Flows