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Convergence of vortex methods for weak solutions to the 2‐D euler equations with vortex sheet data
Author(s) -
Liu JianGuo,
Xin Zhouping
Publication year - 1995
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160480603
Subject(s) - euler equations , vorticity , vortex , vortex sheet , mathematics , smoothing , convergence (economics) , bounded function , mathematical analysis , euler's formula , physics , mechanics , statistics , economics , economic growth
We prove the convergence of vortex blob methods to classical weak solutions for the two‐dimensional incompressible Euler equations with initial data satisfying the conditions that the vorticity is a finite Radon measure of distinguished sign and the kinetic energy is locally bounded. This includes the important example of vortex sheets. The result is valid as long as the computational grid size h does not exceed the smoothing blob size ε, i.e., h /ε ≦ C. . ©1995 John Wiley & Sons, Inc.