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Revista Colombiana de Matemáticas

Print version ISSN 0034-7426

Rev.colomb.mat. vol.43 no.1 Bogotá Jan./June 2009

 

On some properties of the solutions of the problem modelling stratified ocean and atmosphere flows in the half-space

Sobre algunas propiedades asintóticas de las soluciones del problema de modelado estratificado de los flujos del océano y de la atmósfera en el semi-espacio

ANDREI GINIATOULLINE1, ÉDGAR MAYORGA2

1Universidad de los Andes, Bogotá, Colombia. Email: aginiato@uniandes.edu.co
2Universidad de los Andes, Bogotá, Colombia. Email: ed-mayor@uniandes.edu.com


Abstract

We obtain a solution of the initial boundary value problem in the 3-dimensional half-space for a system of an exponentially stratified fluid in the gravity field. We prove the uniqueness of the weak solution in the class of growing functions. We also investigate the asymptotic behavior for the solution as t→ ∞ .

Key words: Partial differential equations, weak solution, Fourier transform, stratified fluid, internal waves, generalized functions.


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

Resumen

Para el sistema de ecuaciones en derivadas parciales que modela el movimiento del líquido exponencialmente estratificado en el campo gravitacional, se soluciona el problema de frontera de valor inicial para el semi-espacio tridimensional. Se prueba la unicidad de la solución débil en una clase de funciones crecientes. También se investiga el comportamiento asintótico de la solución cuando t→ ∞ .

Palabras clave: Ecuaciones en derivadas parciales, solución débil, la transformada de Fourier, líquido estratificado, ondas internas, funciones generalizadas..


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References

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(Recibido en mayo de 2008. Aceptado en marzo de 2009)

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

@ARTICLE{RCMv43n1a05,
    AUTHOR  = {Giniatoulline, Andrei and Mayorga, Édgar},
    TITLE   = {{On some properties of the solutions of the problem modelling stratified ocean and atmosphere flows in the half-space}},
    JOURNAL = {Revista Colombiana de Matemáticas},
    YEAR    = {2009},
    volume  = {43},
    number  = {1},
    pages   = {43-54}
}

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