Opened Access Interface evolution: water waves in 2-D


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Autor: Córdoba Barba, Antonio
Córdoba Gazolaz, Diego
Gancedo García, Francisco
Departamento: Universidad de Sevilla. Departamento de Análisis Matemático
Fecha: 2010-01-15
Publicado en: Advances in Mathematics, 223 (1), 120-173.
Tipo de documento: Artículo
Resumen: We study the free boundary evolution between two irrotational, incompressible and inviscid fluids in 2-D without surface tension. We prove local-existence in Sobolev spaces when, initially, the difference of the gradients of the pressure in the normal direction has the proper sign, an assumption which is also known as the Rayleigh-Taylor condition. The well-posedness of the full water wave problem was first obtained by S. Wu. Well-posedness in Sobolev spaces of the full water wave problem in 2-D. Invent. math. 130, 39-72, 1997. The methods introduced in this paper allows us to consider multiple cases: with or without gravity, but also a closed boundary or a periodic boundary with the fluids placed above and below it. It is assumed that the initial interface does not touch itself, being a part of the evolution problem to check that such property prevails for a short time, as well as it does the Rayleigh-Taylor condition, depending conveniently upon the initial data. The addition of...
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Cita: Córdoba Barba, A., Córdoba Gazolaz, D. y Gancedo García, F. (2010). Interface evolution: water waves in 2-D. Advances in Mathematics, 223 (1), 120-173.
Tamaño: 350.5Kb
Formato: PDF


DOI: 10.1016/j.aim.2009.07.016

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