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2019 (English)In: Entropy, ISSN 1099-4300, E-ISSN 1099-4300, Vol. 21, no 11, p. 1-20, article id 1129Article in journal (Refereed) Published
Abstract [en]
P-adic numbers serve as the simplest ultrametric model for the tree-like structures arisingin various physical and biological phenomena. Recently p-adic dynamical equations started to beapplied to geophysics, to model propagation of fluids (oil, water, and oil-in-water and water-in-oilemulsion) in capillary networks in porous random media. In particular, a p-adic analog of theNavier–Stokes equation was derived starting with a system of differential equations respectingthe hierarchic structure of a capillary tree. In this paper, using the Schauder fixed point theoremtogether with the wavelet functions, we extend the study of the solvability of a p-adic field analogof the Navier–Stokes equation derived from a system of hierarchic equations for fluid flow in acapillary network in porous medium. This equation describes propagation of fluid’s flow throughGeo-conduits, consisting of the mixture of fractures (as well as fracture’s corridors) and capillarynetworks, detected by seismic as joint wave/mass conducts. Furthermore, applying the Adomiandecomposition method we formulate the solution of the p-adic analog of the Navier–Stokes equationin term of series in general form. This solution may help researchers to come closer and find morefacts, taking into consideration the scaling, hierarchies, and formal derivations, imprinted from theanalogous aspects of the real world phenomena.
Place, publisher, year, edition, pages
Basel, Switzerland: MDPI, 2019
Keywords
tree-like geometry; capillary networks; p-adic model of porous medium; fluid’s propagation; complex geological phenomena; p-adic analog of Navier–Stokes equation; pseudo-differential equations; p-adic wavelet basis; Schauder fixed point theorem; Vladimirov’s operator; existence of solution
National Category
Other Mathematics
Research subject
Mathematics, Mathematics; Mathematics, Applied Mathematics
Identifiers
urn:nbn:se:lnu:diva-90573 (URN)10.3390/e21111129 (DOI)000502145000102 ()
2019-12-152019-12-152020-01-10Bibliographically approved