Nonlinear stability of planar steady Euler flows associated with semistable solutions of elliptic problems

نویسندگان

چکیده

This paper is devoted to the study of nonlinear stability steady incompressible Euler flows in two dimensions. We prove that a flow nonlinearly stable L p L^p norm vorticity if its stream function semistable solution some semilinear elliptic problem with nondecreasing nonlinearity. The idea proof show such has strict local maximum energy among whose vorticities are rearrangements given function, help an improved version Wolansky and Ghil’s theorem. result can be regarded as extension Arnol’d’s second

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ژورنال

عنوان ژورنال: Transactions of the American Mathematical Society

سال: 2022

ISSN: ['2330-0000']

DOI: https://doi.org/10.1090/tran/8652