Determination of Time Evolution Equations for Hydrodynamic Variables with Arbitrary Initial Data
We provide an alternative approach for generating time evolution equations for local hydrodynamic variables including density, velocity fields, and kinetic energy using a time evolution equation of the single-particle distribution. We hazard a guess that the Boltzmann equation and the Navier-Stokes equation difficulties are both covered by our time evolution equations. These two formulations might both benefit from the usage of our time evolution equations. In fact, rewriting various applications of the outdated Navier-Stokes equation and Boltzmann equation using our time evolution strategy would be quite fruitful. It is suggested that the prescription, when applied to different pairing potentials between monoatoms, geometry, and starting data, will have many applications in hydrodynamics, including solutions to the Navier-Stokes equation.
Program in Mathematics, Graduate Center, City University of New York, 506 Fifth Avenue, NY 10016, United States.
Please see the link here: https://stm.bookpi.org/NTPSR-V7/article/view/7788
Keywords: Time evolution equations, arbitrary initial data, field velocities, pressure kinetic energy, solutions of navier–stokes equation