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Revista Colombiana de Matemáticas

Print version ISSN 0034-7426

Rev.colomb.mat. vol.41 no.2 Bogotá July/Dec. 2007

 

Spectral properties of compressible stratified flows

Propiedades espectrales de los flujos estratificados comprimibles

ANDREI GINIATOULLINE1, CÉSAR HERNÁNDEZ2

1Universidad de los Andes, Bogotá, Colombia. Email: aginiato@uniandes.edu.co
2Universidad de los Andes, Bogotá, Colombia. Email: cesa-her@uniandes.edu.co


Abstract

For bounded and unbounded domains in R3, we establish the localization and the structure of the spectrum of normal vibrations described by systems of partial differential equations modelling small displacements of compressible stratified fluid in the homogeneous gravity field. We also compare the spectral properties of gravitational and rotational operators. Our main result is the construction of Weyl sequence for the essential spectrum, which is an explicit form of non-uniqueness of the solutions.

Key words: Partial differential equations, essential spectrum, Sobolev spaces, stratified fluid, internal waves.


2000 Mathematics Subject Classification: 35Q35, 35B05, 35P05, 76O26.

Resumen

Para los dominios acotados y no-acotados en R3, estudiamos la localización y la estructura del espectro de las vibraciones normales que se describen mediante sistemas de ecuaciones en derivadas parciales que modelan los movimientos pequeños de un líquido estratificado comprensible en el campo gravitacional homogéneo. También comparamos las propiedades espectrales de los operadores rotacionales y gravitacionales. Nuestro resultado principal es la construcción de la sucesión de Weyl para el espectro esencial, la cual representa explícitamente la no-unicidad de las soluciones.

Palabras clave: Ecuaciones diferenciales parciales, espectro esencial, espacios de Sobolev, líquido estratificado, ondas internas.


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(Recibido en octubre de 2006. Aceptado en septiembre de 2007)

Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:

@ARTICLE{GiniatoullineHernández07,
    AUTHOR = {Andrei Giniatoulline and César Hernández},
    TITLE = {{Spectral properties of compressible stratified flows}},
    JOURNAL = {Revista Colombiana de Matemáticas},
    YEAR = {2007},
    volume = {41},
    number = {2},
    pages = {333-344}
}

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