Convergence for a vortex method for solving Euler's equation

Author:
Theodore E. Dushane

Journal:
Math. Comp. **27** (1973), 719-728

MSC:
Primary 76.65

DOI:
https://doi.org/10.1090/S0025-5718-1973-0339675-6

MathSciNet review:
0339675

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Abstract | References | Similar Articles | Additional Information

Abstract: We consider a new vortex approximation for solving the initial-value problem for the Euler equations in two dimensions. We assume there exists a smooth solution to these equations and that the vorticity has compact support. Then we show that our approximation to the velocity field converges uniformly in space and time for a short time interval.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1973-0339675-6

Keywords:
Vortex approximation,
Euler's equation,
two dimensions,
incompressible fluid flow,
convergence proof

Article copyright:
© Copyright 1973
American Mathematical Society