On the blow-up of solutions of the 3-D Euler equations in a bounded domain
type: Item
instance of: scholarly article
title: On the blow-up of solutions of the 3-D Euler equations in a bounded domain
zbMATH Open document ID: 0787.35071
DOI: 10.1007/BF02097394
author: Andrew B. Ferrari
published in: Communications in Mathematical Physics
publication date: 1994-05-19T00:00:00Z
review text: A problem with the Euler equations for incompressible flow is that it is not known whether its smooth solution persists for all time or it turns to be singular at some later time. It is believed that it should become singular as a result of the development of turbulence in the flow. In the present paper, it is shown that if \((0,T)\) is the maximal interval of existence for such a solution on a bounded domain, then the integral of the \(L\)-infinite norm of its vorticity over this domain is infinite. The proof of this result is based on the application of the theory of linear elliptic systems of partial differential equations to a certain elliptic system associated with Euler equations.
reviewed by: Guy Jumarie
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 76B47
zbMATH DE Number: 459102
zbMATH Keywords: Euler equations
zbMATH Keywords: incompressible flow
zbMATH Keywords: turbulence
zbMATH Keywords: bounded domain
zbMATH Keywords: elliptic system
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 459102