Further remarks on simple flows of fluids with pressure-dependent viscosities

Recently Suslov and Tran (2008) [1] claimed to have found an error in one of the solutions given in the paper by Hron (2001) et al. [2] concerning the flows of fluids with pressure-dependent viscosities. We show that their arguments are related to the question of the continuity of the pressure, and we show that the original solution, although it is not a classical one, can be interpreted as a solution in a generalized sense. Mathematical and physical implications of such generalizations are briefly discussed. The discussion in the paper highlights the importance of recognizing what is meant by a “solution” to a partial differential equation, whether by a solution we mean a classical solution, a weak solution, or a solution in some other sense.