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Commutator estimates, Besov spaces and scattering problems for the acoustic wave propagation in perturbed stratified fluids

Published online by Cambridge University Press:  01 January 2000

BO ZHANG
BO ZHANG
Affiliation:
School of Mathematical and Information Sciences, Coventry University, Coventry CV1 5FB
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Abstract

Mourre's commutator method is used together with Besov spaces, in this paper, to settle the question of uniqueness of solutions to the scattering problem for the acoustic wave propagation in perturbed stratified fluids in Rn with n [ges ] 2: The uniqueness of solutions is established by introducing a radiation condition in the framework of Besov spaces, and is then used to prove resolvent estimates in the Besov space setting for the acoustic propagator in perturbed stratified fluids. These estimates are ‘sharp’ in a sense made precise in the text and are important in establishing existence of solutions to the scattering problem.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 128 , Issue 1 , January 2000 , pp. 177 - 192
Copyright
The Cambridge Philosophical Society 2000

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