Statistical solutions of the two-dimensional incompressible Euler equations in spaces of unbounded vorticity

Wagner R, Wiedemann E (2023)

Publication Type: Journal article

Publication year: 2023

Journal

Journal of Functional Analysis Elsevier

Book Volume: 284

Article Number: 109777

Journal Issue: 4

DOI: 10.1016/j.jfa.2022.109777

Abstract

We study statistical solutions of the incompressible Euler equations in two dimensions with vorticity in Lp, 1≤p≤∞, and in the class of vortex-sheets with a distinguished sign. Our notion of statistical solution is based on the framework due to Bronzi, Mondaini and Rosa in [4]. Existence in this setting is shown by approximation with discrete measures, concentrated on deterministic solutions of the Euler equations. Additionally, we provide arguments to show that the statistical solutions of the Euler equations may be obtained in the inviscid limit of statistical solutions of the incompressible Navier-Stokes equations. Uniqueness of trajectory statistical solutions is shown in the Yudovich class.

Authors with CRIS profile

Emil Wiedemann

Involved external institutions

Universität Ulm DE Germany (DE)

How to cite

APA:

Wagner, R., & Wiedemann, E. (2023). Statistical solutions of the two-dimensional incompressible Euler equations in spaces of unbounded vorticity. Journal of Functional Analysis, 284(4). https://dx.doi.org/10.1016/j.jfa.2022.109777

MLA:

Wagner, Raphael, and Emil Wiedemann. "Statistical solutions of the two-dimensional incompressible Euler equations in spaces of unbounded vorticity." Journal of Functional Analysis 284.4 (2023).

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