Global Existence of Some Infinite Energy Solutions for a Perfect Incompressible Fluid

@article{Saxton2008GlobalEO,
  title={Global Existence of Some Infinite Energy Solutions for a Perfect Incompressible Fluid},
  author={Ralph Saxton and Feride Tiglay},
  journal={SIAM J. Math. Analysis},
  year={2008},
  volume={40},
  pages={1499-1515}
}
This paper provides results on local and global existence for a class of solutions to the Euler equations for an incompressible, inviscid fluid. By considering a class of solutions which exhibits a characteristic growth at infinity we obtain an initial value problem for a nonlocal equation. We establish local well-posedness in all dimensions and persistence in time of these solutions for three and higher dimensions. We also examine a weaker class of global solutions. 

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