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Nonlinear stability of planar steady Euler flows associated with semistable solutions of elliptic problems.
- Source :
-
Transactions of the American Mathematical Society . Jul2022, Vol. 375 Issue 7, p5071-5095. 25p. - Publication Year :
- 2022
-
Abstract
- This paper is devoted to the study of nonlinear stability of steady incompressible Euler flows in two dimensions. We prove that a steady Euler flow is nonlinearly stable in L^p norm of the vorticity if its stream function is a semistable solution of some semilinear elliptic problem with nondecreasing nonlinearity. The idea of the proof is to show that such a flow has strict local maximum energy among flows whose vorticities are rearrangements of a given function, with the help of an improved version of Wolansky and Ghil's stability theorem. The result can be regarded as an extension of Arnol'd's second stability theorem. [ABSTRACT FROM AUTHOR]
- Subjects :
- *STREAM function
*INCOMPRESSIBLE flow
*VORTEX motion
*EULER equations
Subjects
Details
- Language :
- English
- ISSN :
- 00029947
- Volume :
- 375
- Issue :
- 7
- Database :
- Academic Search Index
- Journal :
- Transactions of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 157430866
- Full Text :
- https://doi.org/10.1090/tran/8652