Ideal incompressible fluid motion in domains with edges. I
type: Item
instance of: scholarly article
title: Ideal incompressible fluid motion in domains with edges. I
zbMATH Open document ID: 0603.76022
author: Wojciech M. Zajączkowski
published in: Bulletin of the Polish Academy of Sciences. Technical Sciences
publication date: 1985-01-01T00:00:00Z
review text: The author considers the transient Euler equations for a bounded domain in \({\mathbb{R}}^ 3\) with impermeable walls whose tangential velocity is prescribed. A forcing term is admitted in the equations of motion. Whereas existence and uniqueness of solutions is well known in the case of smooth boundaries, he shows regularity properties of solutions in neighborhoods of edges. By use of alternative approaches, he establishes two upper bounds for the angle defining the edge. The proofs (in weighted Sobolev spaces) are confined to sufficiently small intervals of time. The proofs employ sequences of well-posed auxiliary problems and pertain to weakly convergent successive approximations. Details of proofs are omitted.
Mathematics Subject Classification ID: 76B99
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 35D05
zbMATH DE Number: 3974527
zbMATH Keywords: transient Euler equations
zbMATH Keywords: bounded domain
zbMATH Keywords: impermeable walls
zbMATH Keywords: forcing term
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: smooth boundaries
zbMATH Keywords: regularity
zbMATH Keywords: neighborhoods of edges
zbMATH Keywords: weighted Sobolev spaces
zbMATH Keywords: weakly convergent successive approximations
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description: scientific article; zbMATH DE number 3974527