Regularity of a Weak Solution to the Navier-Stokes Equations via One Component of a Spectral Projection of Vorticity

2012/07/16 by Jiri Neustupa, Neustupa, Jiri, Patrick Penel +1
Mathematics · #35Q30 #76D03 #76D05 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35Q30 #msc:76D03 #msc:76D05

paper · pdf · doi:10.48550/arxiv.1207.3692

16 pages

arxiv created 2012/07/16 · arxiv updated 2012/07/17

Abstract

We deal with a weak solution v to the Navier-Stokes initial value problem in R³ x(0,T). We denote by ω⁺ a spectral projection of ω=\curl v, defined by means of the spectral resolution of identity associated with the self-adjoint operator \curl. We show that certain conditions imposed on ω⁺ or, alternatively, only on ω⁺₃ (the third component of ω⁺) imply regularity of solution v.

Related

• On the Regularity for 3D Navier-Stokes Equation
• New Approach for Vorticity Estimates of Solutions of the Navier-Stokes Equations
• Some remarks on the partial regularity of a suitable weak solution to the Navier-Stokes Cauchy problem
• A new proof of the Théorème de Structure related to a weak solution to the Navier-Stokes equations
• Regularity Conditions of 3D Navier-Stokes flow in terms of large spectral components