Compressible flow and Euler's equations (Q2925172)

The authors consider the classical compressible Euler's equations in three space dimensions with an arbitrary equation of state. The main purpose is to derive qualitative results for the classical, non-relativistic, compressible Euler's equations taking the data to be irrotational and isentropic. Furthermore, the authors present proofs of these results which are simple and completely self-contained. They also present some new results sharper as previous ones. In addition, the monograph explains in depth the ideas on which the given approach is based. Finally, certain geometric aspects are discussed which pertain only to the non-relativistic theory.NEWLINENEWLINEThe book consists of nineteen chapters: 1. Compressible fluids and nonlinear wave equations; 2. The basic geometric construction; 3. The acoustical structure equations; 4. The acoustical curvature; 5. The fundamental energy estimate; 6. Construction of commutation vector fields; 7. Outline of the derived estimates of each order; 8. Regularization of the propagation equation; 9. Regularization of the propagation equation; 10. Control of the angular derivatives of the first derivatives of \(\xi\); 11. Control of the spatial derivatives of the first derivatives; 12. Recovery of the acoustical assumptions. Estimates for up to the next to the top order angular derivatives; 13. Derivation of the basic properties of \(\mu\); 14. The error estimates involving the top order spatial derivatives of the acoustical entities; 15. The top order energy estimates; 16. The descent scheme; 17. The isoperimetric inequality; 18. Sufficient conditions on the initial data for the formation of a shock in the evolution; 19. The structure of the boundary of the domain of the maximal solution.