Continuum and discrete hydrodynamical models and globally well-posed problems

摘要

Two models for one-dimensional hydrodynamical motion are model C and model D. Model C is the standard, classical, continuum model. Well-posedness proofs for problems based on model C encounter extreme technical difficulties. There are dubious steps in the derivation of model C from first principles. Model D is a modification of model C which avoids these dubious steps. A mixed, initial–boundary-value problem based on model D is properly posed globally. The proof presented here is for the pressure obeying a generalization of the ideal-gas law and a viscous stress obeying a generalization of the Navier-Stokes form. No assumptions requiring the initial data to be small deviations from a constant state are required; the initial data are only required to be physically acceptable.