Determining Map, Data Assimilation and an Observable Regularity Criterion for the Three-Dimensional Boussinesq System
dc.contributor.author | Balakrishna, Abhishek | |
dc.contributor.author | Biswas, Animikh | |
dc.date.accessioned | 2023-10-18T15:33:57Z | |
dc.date.available | 2023-10-18T15:33:57Z | |
dc.date.issued | 2022-09-13 | |
dc.description.abstract | In 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.uri | https://link.springer.com/article/10.1007/s00245-022-09896-7 | en_US |
dc.format.extent | 41 pages | en_US |
dc.genre | journal articles | en_US |
dc.genre | preprints | en_US |
dc.identifier | doi:10.13016/m2d6r9-rtrv | |
dc.identifier.citation | Balakrishna, 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/s00245-022-09896-7 | en_US |
dc.identifier.uri | https://doi.org/10.1007/s00245-022-09896-7 | |
dc.identifier.uri | http://hdl.handle.net/11603/30268 | |
dc.language.iso | en_US | en_US |
dc.publisher | Springer | en_US |
dc.relation.isAvailableAt | The University of Maryland, Baltimore County (UMBC) | |
dc.relation.ispartof | UMBC Mathematics Department Collection | |
dc.relation.ispartof | UMBC Faculty Collection | |
dc.relation.ispartof | UMBC Student Collection | |
dc.rights | This 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.title | Determining Map, Data Assimilation and an Observable Regularity Criterion for the Three-Dimensional Boussinesq System | en_US |
dc.type | Text | en_US |
dcterms.creator | https://orcid.org/0000-0003-4411-2891 | en_US |
dcterms.creator | https://orcid.org/0000-0001-8594-0568 | en_US |