Even at the nanoscale, continuum mechanics can be used to describe some phenomena. The Navier-Stokes equations, for example, are used to model fluid dynamics: \[ \rho \left( \frac{\partial \mathbf{u}}{\partial t} + \mathbf{u} \cdot \nabla \mathbf{u} \right) = -\nabla p + \mu \nabla^2 \mathbf{u} + \mathbf{f} \] where \( \rho \) is the fluid density, \( \mathbf{u} \) is the velocity field, \( p \) is pressure, \( \mu \) is the dynamic viscosity, and \( \mathbf{f} \) is the body force. These equations are particularly useful in microfluidics and nanofluidics applications.
