FUNCTIONAL AND MEASURE-VALUED SOLUTIONS OF THE EULER EQUATIONS FOR FLOWS OF INCOMPRESSIBLE FLUIDS
- Authors
- CHAE, DH; DUBOVSKII, P
- Issue Date
- Dec-1995
- Publisher
- SPRINGER VERLAG
- Citation
- ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, v.129, no.4, pp 385 - 396
- Pages
- 12
- Journal Title
- ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
- Volume
- 129
- Number
- 4
- Start Page
- 385
- End Page
- 396
- URI
- https://scholarworks.bwise.kr/cau/handle/2019.sw.cau/57108
- DOI
- 10.1007/BF00379261
- ISSN
- 0003-9527
1432-0673
- Abstract
- We consider the notion of a functional solution of the Euler equations for incompressible fluid flows. We show that a functional solution can be constructed under ''very weak'' a priori estimates on approximate solution sequences of the equation; an estimate uniform in L(loc)(1) together with weak consistency with the equation is sufficient to construct a solution. We prove that if we have an estimate uniform in L(loc)(2) available for the approximate solution sequence, then the structured functional solution just described becomes a measure-valued solution in the sense of DIPERNA & MAJDA. We also show that a functional solution can be obtained from a measure-valued solution. We give an example showing that a much higher concentration of energy than in the case of measure-valued solutions is allowed by the approximation procedure of a functional solution.
- Files in This Item
- There are no files associated with this item.
- Appears in
Collections - College of Natural Sciences > Department of Mathematics > 1. Journal Articles
Items in ScholarWorks are protected by copyright, with all rights reserved, unless otherwise indicated.