Determining Map, Data Assimilation and an Observable Regularity Criterion for the Three-Dimensional Boussinesq System

dc.contributor.authorBalakrishna, Abhishek
dc.contributor.authorBiswas, Animikh
dc.date.accessioned2023-10-18T15:33:57Z
dc.date.available2023-10-18T15:33:57Z
dc.date.issued2022-09-13
dc.description.abstractIn this paper, we consider the analysis of a nudging based algorithm for data assimilation for the three-dimensional Boussinesq system, which we call the AOT system. A rigorous analysis of this algorithm for well-posed dissipative partial differential equations was first provided by Azouani, Olson and Titi (J Nonlinear Sci 24:277–304, 2014); thus justifying our terminology for the associated nudging system. We provide a sufficient condition, based solely on the observed velocity data obtained from a Leray-Hopf weak solution, for the global well-posedness, regularity and most crucially, the asymptotic tracking property of solutions of the associated (three-dimensional) nudging system. It is to be noted that neither regularity nor any knowledge of a uniform ℍ¹-norm bound is a priori assumed on the solution of the original three-dimensional Boussinesq system from which the observations are obtained. As a corollary of our result, we obtain a novel observable regularity criterion based on finitely many observational data. Our condition also guarantees the construction of the Lipschitz continuous determining map, which is known to play a crucial role in the construction of the so-called determining form and in statistical data assimilation.en_US
dc.description.urihttps://link.springer.com/article/10.1007/s00245-022-09896-7en_US
dc.format.extent41 pagesen_US
dc.genrejournal articlesen_US
dc.genrepreprintsen_US
dc.identifierdoi:10.13016/m2d6r9-rtrv
dc.identifier.citationBalakrishna, A., Biswas, A. Determining Map, Data Assimilation and an Observable Regularity Criterion for the Three-Dimensional Boussinesq System. Appl Math Optim 86, 28 (2022). https://doi.org/10.1007/s00245-022-09896-7en_US
dc.identifier.urihttps://doi.org/10.1007/s00245-022-09896-7
dc.identifier.urihttp://hdl.handle.net/11603/30268
dc.language.isoen_USen_US
dc.publisherSpringeren_US
dc.relation.isAvailableAtThe University of Maryland, Baltimore County (UMBC)
dc.relation.ispartofUMBC Mathematics Department Collection
dc.relation.ispartofUMBC Faculty Collection
dc.relation.ispartofUMBC Student Collection
dc.rightsThis item is likely protected under Title 17 of the U.S. Copyright Law. Unless on a Creative Commons license, for uses protected by Copyright Law, contact the copyright holder or the author.en_US
dc.titleDetermining Map, Data Assimilation and an Observable Regularity Criterion for the Three-Dimensional Boussinesq Systemen_US
dc.typeTexten_US
dcterms.creatorhttps://orcid.org/0000-0003-4411-2891en_US
dcterms.creatorhttps://orcid.org/0000-0001-8594-0568en_US

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