We consider the motion of a fluid exterior to a moving rigid obstacle, or interior to a moving rigid shell. The boundary conditions, such as the no-slip condition and the condition of an isothermal wall, applied in the solution of the system of differential equations describing these motions, are currently assumed to be an approximation derived from experimental observation rather than an exact law. It is the purpose of this paper to show that the boundary conditions at a material interface between a fluid and a solid are derivable from the global principles of balance of continuum mechanics and the Clausius-Duhem inequality.


Navier-Stokes equations, boundary conditions, entropy condition


Applied Mathematics | Mechanics of Materials


American Mathematical Society

Publication Date


Rights Information

First published in Quarterly of Applied Mathematics in v.53 no.3 (Sept. 2005), published by the American Mathematical Society

Rights Holder

© 2005 Brown University

figure1.zip (1854 kB)

Click button above to open, or right-click to save.

Additional Files

figure1.zip (1854 kB)