Abstract
In this paper, we consider an inviscid, incompressible, irrotational fluid in a region of R 3 with free boundary. Motivated by [1], we find that in this particular case, we do not need the complicated energy functional in [1], instead we can use a simpler replacement and get the a priori energy estimate for a positive time, which depends only on the initial data.
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Chen, Ym. On the Free Boundary to the Incompressible Euler Equations. Acta Mathematicae Applicatae Sinica, English Series 21, 389–398 (2005). https://doi.org/10.1007/s10255-005-0246-7
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DOI: https://doi.org/10.1007/s10255-005-0246-7