Highly Influenced

4 Excerpts

@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} }

- Published in SIAM J. Math. Analysis 2008
DOI:10.1137/080713768

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.