On some regularity results for the stationary Stokes system and the 2-\(D\) Euler equations
type: Item
instance of: scholarly article
title: On some regularity results for the stationary Stokes system and the 2-\(D\) Euler equations
zbMATH Open document ID: 1348.35179
DOI: 10.4171/PM/1969
author: H. Beirão da Veiga
published in: Portugaliae Mathematica. Nova Série
publication date: 2016-06-23T00:00:00Z
review text: Summary: We revisit ``minimal assumptions'' on the data which guarantee that solutions to the 2-\(D\) evolution Euler equations in a bounded domain are classical. Classical means here that all the derivatives appearing in the equations and boundary conditions are continuous up to the boundary. Following a well known device, the above problem led us to consider this same regularity problem for the Poisson equation under homogeneous Dirichlet boundary conditions. At this point, one was naturally led to consider the extension of this last problem to more general linear elliptic boundary value problems, and also to try to extend the results to more general data spaces. Pursuing and developing results that remained unpublished about thirty years, we survey the route followed in the study of these problems and we consider new results and open problems. In particular, we extend some minimal assumption results for the stationary Stokes system, and for and for the planar, evolution, Euler equations, to larger data spaces.
Mathematics Subject Classification ID: 35Q31
Mathematics Subject Classification ID: 26B30
Mathematics Subject Classification ID: 26B35
Mathematics Subject Classification ID: 35A09
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 76D07
zbMATH DE Number: 6597545
zbMATH Keywords: linear elliptic boundary value problems
zbMATH Keywords: Stokes system
zbMATH Keywords: Euler equations
zbMATH Keywords: classical solutions
zbMATH Keywords: continuity of higher order derivatives
zbMATH Keywords: functional spaces
zbMATH Keywords: Dini's continuity
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4171/pm/1969
OpenAlex ID: W2341231721
description: scientific article; zbMATH DE number 6597545