Abstract
Revision of the mathematical formalism of fluid dynamics suggests that some physical inconsistencies (infinite time of approaching equilibrium and fully deterministic solutions to the Navier-Stokes equations) can be removed by relaxing the Lipschitz conditions, i.e., the boundedness of the derivatives, in the constitutive equations. Physically such a modification can be interpreted as an incorporation of an infinitesimal static friction in the constitutive law. A modified version of the Navier-Stokes equations is introduced, discussed, and illustrated by examples. It is demonstrated that all the new effects in the modified model emerge within vanishingly small neighborhoods of equilibrium states which are the only domains where the governing equations are different from classical.
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References
Landau, L. D., and Lifshitz, E. M. (1953).Fluid Mechanics, Pergamon Press, Oxford.
Zak, M. (1992). The problem of irreversibility in Newtonian dynamics.International Journal of Theoretical Physics, 31(2), 332–342.
Zak, M. (1993a). Terminal model of Newtonian dynamics,International Journal of Theoretical Physics. 32(1), 159–190.
Zak, M. (1993b). Introduction to terminal dynamics,Complex Systems, 7(1), 59–87.
Ziegler, H. (1963).Some Extremum Principles in Irreversible Thermodynamics with Application to Continuum Mechanics, North-Holland, Amsterdam.
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Zak, M., Meyers, R.E. Non-Newtonian effects in viscous flows. Int J Theor Phys 35, 1423–1460 (1996). https://doi.org/10.1007/BF02084951
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DOI: https://doi.org/10.1007/BF02084951