Travelling wave-like solutions of the Navier-Stokes and the related equations
- Authors
- Chae, D; Dubovskii, P
- Issue Date
- Dec-1996
- Publisher
- ACADEMIC PRESS INC JNL-COMP SUBSCRIPTIONS
- Citation
- JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, v.204, no.3, pp 930 - 939
- Pages
- 10
- Journal Title
- JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
- Volume
- 204
- Number
- 3
- Start Page
- 930
- End Page
- 939
- URI
- https://scholarworks.bwise.kr/cau/handle/2019.sw.cau/57107
- DOI
- 10.1006/jmaa.1996.0477
- ISSN
- 0022-247X
1096-0813
- Abstract
- We present a new family of travelling wave-like solutions to the Navier-Stokes equations of incompressible fluid flows, and other regularized equations of the Euler equations, obtain their trend to the solutions of the Euler equations as the viscosity tends to zero, and estimate the rate of convergence. We also find a ''singularizing effect'' of the viscosity term in the Navier-Stokes equations, i.e., we have a local moving blow-up of unbounded solutions with the blow-up's speed depending on viscosity. We demonstrate that if the initial function is the Beltrami flow then the solution of the Navier-Stokes equations conserves the Beltrami flow property for all time. (C) 1996 Academic Press, Inc.
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Collections - College of Natural Sciences > Department of Mathematics > 1. Journal Articles
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