Continuum and discrete hydrodynamical models and globally well-posed problems
Document Type
Article
Publication Date
3-1988
Department
Department of Mathematical Sciences
Abstract
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.
Publication Title
Applied Mathematics and Computation
Recommended Citation
Hicks, D.,
&
Kuttler, K.
(1988).
Continuum and discrete hydrodynamical models and globally well-posed problems.
Applied Mathematics and Computation,
25(4), 299-320.
http://doi.org/10.1016/0096-3003(88)90126-9
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/5570
