Covariant Formulation of Fluid Dynamics and Estakhr’s Material Geodesic Equation,

When i meet God, I am going to ask him two questions, why relativity and why turbulence. A. Einstein

You probably will not need to ask these questions of God, I’ve already answered both of them. $U^{\mu}=\gamma (c,u(\vec {r}, t))$ denotes four-velocity field. $J^ {\mu}=\rho U^{\mu}$ denotes four-current mass density. Estakhr’s Material-Geodesic equation is developed analogy of Navier Stokes equation and Einstein Geodesic equation. $\frac{DJ^ {\mu}}{D\tau}=\frac{dJ^{\mu}}{D \tau}+\Gamma^{\mu}_{\alpha \beta}J^{\alpha}U^{\beta}=J_ {\nu}\Omega^{\mu\nu}+\partial_ {\nu}T^{\mu\nu}+\Gamma^{\mu} _{\alpha\beta}J^{\alpha}U^ {\beta}$
Fluid dynamic of impact
Covariant formulation of fluid dynamics, describe the motion of fluid substances. The local existence and uniqueness theorem for geodesics states that geodesics on a smooth manifold with an affine connection exist, and are unique. EMG equation is also applicable in different branches of physics, it all depend on what you mean by 4-current density, if you mean 4-current electron number density then it is plasma physics, if you mean 4-current electron charge density then it is $\frac{DJ^ {\mu}}{D\tau}=J_{\nu}F^{\mu \nu}+\partial_{\nu}T^{\mu\nu}+ \Gamma^{\mu}_{\alpha\beta}J^ {\alpha}U^{\beta}$ electromagnetism.

Fluid dynamic of impact

While Rocks of Earth’s surface aren’t fluid in our everyday energies, it’s perfectly plausible that they might display fluid-like properties in higher energies.

Reference link:66th Annual Meeting of the APS Division of Fluid Dynamics Volume 58, Number 18

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Author: Mr. ESTAKHR, Ahmad reza

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