On concentration in vortex sheets

Samuel Lanthaler ()
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Samuel Lanthaler: California Institute of Technology

Partial Differential Equations and Applications, 2023, vol. 4, issue 2, 1-39

Abstract: Abstract The question of energy concentration in approximate solution sequences $$u^\epsilon $$ u ϵ , as $$\epsilon \rightarrow 0$$ ϵ → 0 , of the two-dimensional incompressible Euler equations with vortex-sheet initial data is revisited. Building on a novel identity for the structure function in terms of vorticity, the vorticity maximal function is proposed as a quantitative tool to detect concentration effects in approximate solution sequences. This tool is applied to numerical experiments based on the vortex-blob method, where vortex sheet initial data without distinguished sign are considered, as introduced in Krasny (J Fluid Mech 167:65–93, 1986). Numerical evidence suggests that no energy concentration appears in the limit of zero blob-regularization $$\epsilon \rightarrow 0$$ ϵ → 0 , for the considered initial data.

Keywords: 35Q35; 35Q31; 65M12; 65M70; 76B03 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s42985-023-00230-6

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