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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

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Journal:
Communications in Mathematical Physics
Pages:
1-41
Publication date:
2012-01-24
DOI:
EISSN:
1432-0916
ISSN:
0010-3616
Source identifiers:
407497
Keywords:
Pubs id:
pubs:407497
UUID:
uuid:cc99c4e9-1e7b-4d9d-8ddf-75533b9dbc2b
Local pid:
pubs:407497
Deposit date:
2013-11-16

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