Scaling invariant Serrin criterion via one velocity component for the Navier-Stokes equations

2020/05/25 by Wendong Wang, Di Wu, Wang, Wendong +3 · 2 citations
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Combinatorics #Component (thermodynamics) #Compressibility #FOS: Mathematics #Geometry #Invariant (physics) #Mathematical analysis #Mathematical physics #Mathematics #Navier-Stokes equation solutions #Navier–Stokes equations #Nonlinear Partial Differential Equations #Physics #Scaling #Thermodynamics #math.AP

paper · pdf · doi:10.48550/arxiv.2005.11906

openalex publication_date 2020/05/25 · openalex created_date 2020/05/29 · arxiv created 2020/06/07 · arxiv updated 2020/06/09 · openalex updated_date 2026/08/05

Abstract

In this paper, we prove that the Leray weak solution u : ℝ³× (0, T)→ℝ³ of the Navier-Stokes equations is regular in ℝ³× (0,T) under the scaling invariant Serrin condition imposed on one component of the velocity u₃∈ L^q,1(0, T;L^p(ℝ³)) with (2)/(q)+(3)/(p)≤ 1, 3<p<+∞. This result is an immediate consequence of a new local regularity criterion in terms of one velocity component for suitable weak solutions.

Citations

• StrongL p -solutions of the Navier-Stokes equation inR m , with applications to weak solutions
• Regularity criteria for the three-dimensional Navier-Stokes equations
• Quantitative bounds for critically bounded solutions to the Navier-Stokes equations
• On the Serrin-type condition on one velocity component for the Navier-Stokes equations

Cited by

• Prodi--Serrin condition for 3D Navier--Stokes equations via one directional derivative of velocity
• Serrin-type regularity criteria for the 3D MHD equations via one velocity component and one magnetic component

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