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Some considerations on the nonlinear stability of stationary planar Euler flows

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Abstract

We give sufficient conditions for the nonlinear stability of possibly nonsmooth stationary solutions of the two-dimensional Euler equation in symmetric bounded domains. We use, as Lyapunov functions, first integrals due to the symmetry of the problem. Moreover, we investigate the stability of smooth solutions under perturbations of the boundary. The last result is based on a generalization of the well known Arnold approach.

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Authors and Affiliations

  1. Dipartimento di Matematica dell'Università di Trento, I-38050, Povo (Trento), Italy

    C. Marchioro

  2. Dipartimento di Matematica dell'Università di Roma “La Sapienza,”, Piazzale Aldo Moro 2, I-00185, Roma, Italy

    M. Pulvirenti

Authors
  1. C. Marchioro
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  2. M. Pulvirenti
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Additional information

Communicated by J. L. Lebowitz

Research partially supported by Italian CNR and Ministero della Pubblica Istruzione

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Marchioro, C., Pulvirenti, M. Some considerations on the nonlinear stability of stationary planar Euler flows. Commun.Math. Phys. 100, 343–354 (1985). https://doi.org/10.1007/BF01206135

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  • DOI: https://doi.org/10.1007/BF01206135

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