Hydrodynamic singularities

Sink Flow Deforms the Interface Between a Viscous Liquid and Air into a Tip Singularity

“…Mathematically, all the above phenomena correspond to a singularity [10,11] of an underlying hydrodynamic equation, in which the hydrodynamic fields become non-smooth. Hydrodynamic singularities can be classified into two groups.…”

Critical phenomena and breaking drops: Infinite idealizations in physics

“…7 Often in attempting to reduce a theory T c to T f in the philosopher's sense we find that we need to amend or correct the reduced theory T c . 8 Most physicists, now, would accept the idea that our concept of temperature and our conception of other "exact" terms that appear in classical thermodynamics such as "entropy", need to be modified in light of the alleged reduction to statistical mechanics.…”

“…T * c corrects T c in that it makes more accurate predictions than does T c . 7 Again, Nagel, himself, would take (N) to be a caricature of the position. 8 See [20] and [18].…”

Elements of Similarity and Singularity

“…We exclude to our analysis "trivial" singularities, arising because of a lack of accuracy in the physical description, and not directly related to the structure of the system. Relevant physical singularities are robust with respect to the addition of regularization processes 13 . In the simple case of a shock wave, a discontinuity in pressure, velocity and density, the propagation properties do not depend on the small scale structure of the shock, determined by dissipation processes (heat, viscosity) 29 .…”