The symmetries of slow motions and the equilibria of continua

The spatial fields of the velocities of slow flows of a viscous incompressible fluid and the equilibrium displacements in elastic media are considered within the framework of models of continua which satisfy the Navier-Stokes or Hooke's laws. A unified description of the velocity fields and the displacements is found. The unified equations of the field possess symmetry, and, due to this symmetry, the unified system is related to Laplace's equation. Formulations of boundary-value problems for a symmetric system of equations are proposed. The symmetry of the unified equations of the fields can be used in the numerical method of a boundary integral equation.