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Stochastic stability of invariant measures: The 2D Euler equation

Departamento de Matemática, Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa and Centro de Matemática e Aplicações, Portugal

E-mail Address: [email protected]

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H. Ouerdiane

Départment de Mathématiques, Faculté des Sciences, Université de Tunis El Manar, Campus Universitaire, 1060 Tunis, Tunis

E-mail Address: [email protected]

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and

R. Vilela Mendes

Corresponding author.

CMAFCIO and IPFN, Universidade de Lisboa, C6, 1749-016 Lisboa, Portugal

E-mail Address: [email protected]

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https://doi.org/10.1142/S0217979219501856Cited by:0

Abstract

In finite-dimensional dissipative dynamical systems, stochastic stability provides the selection of the physically relevant measures. That this might also apply to systems defined by partial differential equations, both dissipative and conservative, is the inspiration for this work. As an example, the 2D Euler equation is studied. Among other results this study suggests that the coherent structures observed in 2D hydrodynamics are associated with configurations that maximize stochastically stable measures uniquely determined by the boundary conditions in dynamical space.

Keywords:

PACS: 05.40.Ca, 05.90.+m, 64.90.+b

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Published: 18 July 2019

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Vol. 33, No. 17

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Received 21 February 2019

Revised 15 May 2019

Accepted 16 May 2019

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Stochastic stability of invariant measures: The 2D Euler equation

Abstract

References

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