Abstract
In this paper we give a survey on how to apply recent techniques of Clifford analysis over conformally flat manifolds to deal with instationary flow problems on cylinders and tori. Solutions are represented in terms of integral operators involving explicit expressions for the Cauchy kernel that are associated to the parabolic Dirac operators acting on spinor sections of these manifolds.
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Acknowledgements
The work of the third author is supported by the project Neue funktionentheoretische Methoden für instationäre PDE, funded by Programme for Cooperation in Science between Portugal and Germany, DAAD-PPP Deutschland-Portugal, Ref: 57340281. The work of the first and second authors is supported via the project “New Function Theoretical Methods in Computational Electrodynamics” approved under the agreement Acções Integradas Luso-Alemãs DAAD-CRUP, ref. A-15/17, and by Portuguese funds through the CIDMA - Center for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology (“FCT–Fundação para a Ciência e a Tecnologia”), within project UID/MAT/0416/2013.
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Cerejeiras, P., Kähler, U., Kraußhar, R.S. (2018). Some Applications of Parabolic Dirac Operators to the Instationary Navier-Stokes Problem on Conformally Flat Cylinders and Tori in \(\mathbb {R}^3\). In: Cerejeiras, P., Nolder, C., Ryan, J., Vanegas Espinoza, C. (eds) Clifford Analysis and Related Topics. CART 2014. Springer Proceedings in Mathematics & Statistics, vol 260. Springer, Cham. https://doi.org/10.1007/978-3-030-00049-3_2
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