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The vortex blob method as a second-grade non-Newtonian fluid

Abstract:

We show that a certain class of vortex blob approximations for ideal hydrodynamics in two dimensions can be rigorously understood as solutions to the equations of second-grade non-Newtonian fluids with zero viscosity, and initial data in the space of Radon measures ${\mathcal M}({\mathbb R}^2)$. The solutions of this regularized PDE, also known as the averaged Euler or Euler-$\alpha$ equations, are geodesics on the volume preserving diffeomorphism group with respect to a new weak right invari...

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Journal:
Communications in Partial Differential Equations More from this journal
Volume:
26
Issue:
1-2
Pages:
295-314
Publication date:
1999-10-18
ISSN:
0360-5302
Language:
English
Keywords:
Pubs id:
pubs:404784
UUID:
uuid:f90ad55e-1472-443f-a083-25e58f28a64d
Local pid:
pubs:404784
Source identifiers:
404784
Deposit date:
2013-11-16

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