Global regularity criteria for the Navier-Stokes equations based on one approximate solution

2019/10/12 by Tuan N. Pham, Pham, Tuan N.
Computer Science · Mathematics · Physics and Astronomy · #35B20 (Secondary) #35B65 (Primary) #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical Analysis (math.NA) #cs.NA #math-ph #math.AP #math.MP #math.NA #msc:35B20 #msc:35B65

paper · pdf · doi:10.48550/arxiv.1910.05501

22 pages; some references added

arxiv created 2021/09/01 · arxiv updated 2021/09/02

Abstract

Considering the three-dimensional incompressible Navier-Stokes equations on the whole space, we address the question: is it possible to infer global regularity of a mild solution from a single approximate solution? Assuming a relatively simple scale-invariant relation involving the size of the approximate solution, the resolution parameter, and the initial energy, we show that the answer is affirmative for a general class of approximate solutions, including Leray's mollified solutions. Two different treatments leading to essentially the same conclusion are presented.

Related

• Global regularity for some classes of large solutions to the Navier-Stokes equations
• Global regularity of the Navier-Stokes equation on thin three dimensional domains with periodic boundary conditions
• Global regularity for the Navier-Stokes equations with application to global solvability for the Euler equations
• Localisation and compactness properties of the Navier-Stokes global regularity problem
• Regularity Criteria For Strong Solutions To The 3D Navier-Stokes Equations