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Concentration-cancellation and Hardy spaces

by I. Vecchi

(Report number 1991-03)

Abstract
et $\upsilon^{\in}$ a sequence of DiPerna-Majda approximate solutions to the 2-D incompressible Euler equations. We prove that if the vorticity sequence is weakly compact in the Hardy space $H^1(R^2)$ then a subsequence of $\upsilon^{\in}$ converges strongly in $L^2(R^2)$ to a solution of the Euler equations. This phenomenon is directly related to the cancellation effects exhibited by "phantom vortices".

Keywords: Riesz transform, equibounded, Dunford-Pettis theorem

@Techreport{V91_3,
  author = {I. Vecchi},
  title = {Concentration-cancellation and Hardy spaces},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {1991-03},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports1991/1991-03.pdf },
  year = {1991}
}

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