Lower bounds for possible singular solutions for the Navier--Stokes and Euler equations revisited

2015/03/10 by Jean C. Cortissoz, Cortissoz, Jean C., Julio A. Montero +1
Engineering · Mathematics · #35B44 (Secondary) #35Q30 (Primary) #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Navier-Stokes equation solutions #math.AP #msc:35B44 #msc:35Q30

paper · pdf · doi:10.48550/arxiv.1503.03063

This version includes a previous result for the Navier-Stokes equation and we have added an application to a possible blow-up for Euler equations

openalex publication_date 2015/03/10 · arxiv created 2016/09/02 · arxiv updated 2016/09/06 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

Abstract

In this paper we give optimal lower bounds for the blow-up rate of the H^s(\mathbbT³)-norm, (1)/(2)<s<(5)/(2), of a putative singular solution of the Navier-Stokes equations, and we also present an elementary proof for a lower bound on blow-up rate of the Sobolev norms of possible singular solutions to the Euler equations when s>(5)/(2).

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