On the regularity of the pressure of weak solutions of Navier-Stokes equations
type: Item
instance of: scholarly article
title: On the regularity of the pressure of weak solutions of Navier-Stokes equations
zbMATH Open document ID: 0574.35070
DOI: 10.1007/BF01210782
author: Hermann Sohr
author: Wolf von Wahl
published in: Archiv der Mathematik
publication date: 1986-01-01T00:00:00Z
review text: The aim of this paper is to prove the regularity property \(p\in L^{5/3}\) for the pressure of weak solutions of Navier-Stokes equations in a bounded or an exterior domain. This result was known only for the whole space. The method to prove this property uses a new potential theoretical estimate of the linearized equation with different integration exponents in space and time. Using this regularity property of the pressure, it is possible to prove the existence of a weak solution of Navier-Stokes equations which is smooth for large \(| x|\) in an exterior domain. This result has been proved by \textit{L. Caffarelli}, \textit{R. Kohn} and \textit{L.Nirenberg} [Commun. Pure Appl. Math. 35, 771-831 (1982; Zbl 0509.35067)] for the whole space.
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 35D10
Mathematics Subject Classification ID: 35D05
Mathematics Subject Classification ID: 76D05
zbMATH DE Number: 3916871
zbMATH Keywords: regularity
zbMATH Keywords: pressure of weak solutions
zbMATH Keywords: Navier-Stokes equations
zbMATH Keywords: linearized equation
zbMATH Keywords: existence
zbMATH Keywords: weak solution
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3916871