Statistical solutions of the incompressible Euler equations
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Date
2021-02
Publication Type
Journal Article
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yes
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Abstract
We propose and study the framework of dissipative statistical solutions for the incompressible Euler equations. Statistical solutions are time-parameterized probability measures on the space of square-integrable functions, whose time-evolution is determined from the underlying Euler equations. We prove partial well-posedness results for dissipative statistical solutions and propose a Monte Carlo type algorithm, based on spectral viscosity spatial discretizations, to approximate them. Under verifiable hypotheses on the computations, we prove that the approximations converge to a statistical solution in a suitable topology. In particular, multi-point statistical quantities of interest converge on increasing resolution. We present several numerical experiments to illustrate the theory.
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published
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Journal / series
Volume
31 (02)
Pages / Article No.
223 - 292
Publisher
World Scientific
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Subject
Statistical solutions; Incompressible Euler; Monte Carlo; Structure functions; Energy spectra
Organisational unit
03851 - Mishra, Siddhartha / Mishra, Siddhartha
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Funding
770880 - Computation and analysis of statistical solutions of fluid flow (EC)
Related publications and datasets
Is new version of: http://hdl.handle.net/20.500.11850/364379