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On the finite-time splash and splat singularities for the 3-D free-surface Euler equations

Abstract:

We prove that the 3-D free-surface incompressible Euler equations with regular initial geometries and velocity fields have solutions which can form a finite-time "splash" (or "splat") singularity first introduced in [9], wherein the evolving 2-D hypersurface, the moving boundary of the fluid domain, self-intersects at a point (or on surface). Such singularities can occur when the crest of a breaking wave falls unto its trough, or in the study of drop impact upon liquid surfaces. Our approach ...

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Publisher copy:
10.1007/s00220-013-1855-2

Authors


Coutand, D More by this author
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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Journal:
Communications in Mathematical Physics
Pages:
1-41
Publication date:
2012-01-24
DOI:
EISSN:
1432-0916
ISSN:
0010-3616
URN:
uuid:cc99c4e9-1e7b-4d9d-8ddf-75533b9dbc2b
Source identifiers:
407497
Local pid:
pubs:407497

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