Euler's equations and the maximum principle
- Authors
- Chae, Dongho
- Issue Date
- Feb-2015
- Publisher
- SPRINGER HEIDELBERG
- Keywords
- 35Q31; 76B03; 76W05
- Citation
- MATHEMATISCHE ANNALEN, v.361, no.1-2, pp 51 - 66
- Pages
- 16
- Journal Title
- MATHEMATISCHE ANNALEN
- Volume
- 361
- Number
- 1-2
- Start Page
- 51
- End Page
- 66
- URI
- https://scholarworks.bwise.kr/cau/handle/2019.sw.cau/9892
- DOI
- 10.1007/s00208-014-1063-1
- ISSN
- 0025-5831
1432-1807
- Abstract
- In this paper we use maximum principle in the far field region for the time dependent self-similar Euler equations to exclude discretely self-similar blow-up for the Euler equations of the incompressible fluid flows. Our decay conditions near spatial infinity of the blow-up profile are given explicitly in terms the coefficient in the equations. We also deduce triviality of the discretely self-similar solution to the magnetohydrodynamic system, under suitable decay conditions near spatial infinity than the previous one. Applying similar argument directly to the Euler equations, we obtain a priori estimate of the vorticity in the far field region.
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