Author(s)

Jorge Zabadal¹, Ederson Staudt², Ádnei Marinho³, Vinícius Ribeiro¹

¹Departamento Interdisciplinar do Campus Litoral Norte, Universidade Federal do Rio Grande do Sul (UFRGS), Tramandaí, Brasil.
²Universidade Federal da Fronteira Sul (UFFS)-Campus Chapecó, Chapecó, Brasil.
³Universidade Federal Rural da Amazônia (UFRA)-Campus Parauapebas, Parauapebas, Brasil.

This work presents novel hydrodynamic formulations that reconcile the continuum hypothesis with the emergence of electromagnetic interactions among molecules from fundamental principles. Two models are proposed: a relativistic version of the Navier-Stokes equations derived from commutation relations, and a Helmholtz-like system obtained by applying the Hodge operator to the extended Navier-Stokes equations. Preliminary analysis suggests that the second model, with its nonlinear terms serving as a generalized current, can reproduce microscopic quantum effects. It shows promise for generating self-consistent field equations via B?cklund transformations, remaining valid across all scales despite the breakdown of the continuum hypothesis.

Commutation Relations, Extended Navier-Stokes Equations, Extended Helmholtz Equations, Interaction Terms, Quantum Behavior

Zabadal, J. , Staudt, E. , Marinho, Á. and Ribeiro, V. (2023) Fundamental Connections in Differential Geometry: Quantum Field Theory, Electromagnetism, Chemistry and Fluid Mechanics. Open Access Library Journal, 10, 1-15. doi: 10.4236/oalib.1110192.