Please use this identifier to cite or link to this item: http://hdl.handle.net/10316/44405
Title: On the interior regularity of weak solutions to the 2-D incompressible Euler equations
Authors: Siljander, Juhana 
Urbano, José Miguel 
Issue Date: 2017
Publisher: Springer
Issue Date: 2017
Publisher: Springer
Project: info:eu-repo/grantAgreement/FCT/5876/147205/PT 
Abstract: We study whether some of the non-physical properties observed for weak solutions of the incompressible Euler equations can be ruled out by studying the vorticity formulation. Our main contribution is in developing an interior regularity method in the spirit of De Giorgi–Nash–Moser, showing that local weak solutions are exponentially integrable, uniformly in time, under minimal integrability conditions. This is a Serrin-type interior regularity result \begin{aligned} u \in L_\mathrm{loc}^{2+\varepsilon }(\Omega _T) \implies \mathrm{local\ regularity} \end{aligned} for weak solutions in the energy space L_t^\infty L_x^2, satisfying appropriate vorticity estimates. We also obtain improved integrability for the vorticity—which is to be compared with the DiPerna–Lions assumptions. The argument is completely local in nature as the result follows from the structural properties of the equation alone, while completely avoiding all sorts of boundary conditions and related gradient estimates. To the best of our knowledge, the approach we follow is new in the context of Euler equations and provides an alternative look at interior regularity issues. We also show how our method can be used to give a modified proof of the classical Serrin condition for the regularity of the Navier–Stokes equations in any dimension.
URI: http://hdl.handle.net/10316/44405
Other Identifiers: 10.1007/s00526-017-1231-8
DOI: 10.1007/s00526-017-1231-8
Rights: embargoedAccess
Appears in Collections:I&D CMUC - Artigos em Revistas Internacionais

Files in This Item:
File Description SizeFormat
Urbano_paper10.pdf376.49 kBAdobe PDFView/Open
Show full item record

WEB OF SCIENCETM
Citations

1
checked on Jun 25, 2019

Page view(s) 20

468
checked on Aug 20, 2019

Download(s)

49
checked on Aug 20, 2019

Google ScholarTM

Check

Altmetric

Altmetric


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.