NONLINEAR STABILITY OF PLANAR STEADY EULER FLOWS ASSOCIATED WITH SEMISTABLE SOLUTIONS OF ELLIPTIC PROBLEMS
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 Lp norm of the vorticity if its stream function is a semistable solution of some semilinear elliptic problem with nondecreasing...
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| Format: | Article |
| Language: | English |
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American Mathematical Society
2022
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| Online Access: | View Fulltext in Publisher |
| Summary: | 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 Lp 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. © 2022 American Mathematical Society |
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| ISBN: | 00029947 (ISSN) |
| DOI: | 10.1090/tran/8652 |