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Spectral properties of compressible stratified flows
Propiedades espectrales de los flujos estratificados comprimibles
Mots-clés :
Partial differential equations, Essential spectrum, Sobolev spaces, Stratified fluid, Internal waves, 2000 Mathematics Subject Classification. 35Q35, 35B05, 35P05, 76026 (en)Ecuaciones diferenciales parciales, Espectro esencial, Espacios de Sobolev, Líquido estratificado, Ondas internas (es)
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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.
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.
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