Pinnau, "A note on boundary conditions for quantum hydrodynamic equations
," Applied Mathematics Letters, vol.
The assumption of constant physical properties for the solid and the air allows decoupling the hydrodynamic equations
of heat equations.
To this end, the hydrodynamic equations
were considered in the spirit of two fundamental approaches, the quasi-static and the lubrication approximations.
who formulated a set of hydrodynamic equations
investigating quark-gluon plasma, a state of matter believed to exist right after the Big Bang; and Gabriela Farfan, 18, of Madison, Wis.
The density and viscosity in the hydrodynamic equations
are defined as:
we obtain the final form of the hydrodynamic equations
The code solves the three-dimensional hydrodynamic equations
under the following assumptions:
are nonlinear Reynolds equations with continuously changing boundary conditions.
Thus, considering electroosmotic flow under the limiting case given by Equation (152), the hydrodynamic field is determined as a solution of the boundary value problem given by hydrodynamic Equations
(17) and (18) subject to boundary conditions (153) and (154), at the particle surfaces, and (22), (145) and (146), at the planes A and B (Figure 4).
They derived this description by adding the effects of random, thermal fluctuations to existing hydrodynamic equations