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

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.

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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