The Formation of Shocks in 3-Dimensional Fluids

  • Demetrios Christodoulou

    ETH Zürich, Switzerland
The Formation of Shocks in 3-Dimensional Fluids cover
Buy from $171.00Download PDF

A subscription is required to access this book.

FrontmatterDownload pp. i–v
ContentsDownload pp. vii–viii
Prologue and SummaryDownload pp. 1–21
1Relativistic Fluids and Nonlinear Wave Equations. The Equations of Variationpp. 23–37
2The Basic Geometric Constructionpp. 39–52
3The Acoustical Structure Equationspp. 53–83
4The Acoustical Curvaturepp. 85–98
5The Fundamental Energy Estimatepp. 99–137
6Construction of the Commutation Vectorfieldspp. 139–168
7Outline of the Derived Estimates of Each Orderpp. 169–201
8Regularization of the Propagation Equation for d\cancel{d}trχ\chi. Estimates for the Top Order Angular Derivatives of χ\chipp. 203–273
9Regularization of the Propagation Equation for Δμ\cancel{\Delta}\mu. Estimates for the Top Order Spatial Derivatives of μ\mupp. 275–328
10Control of the Angular Derivatives of the First Derivatives of the xix^i. Assumptions and Estimates in Regard to χ\chipp. 329–472
11Control of the Spatial Derivatives of the First Derivatives of the xix^i. Assumptions and Estimates in Regard to μ\mupp. 473–664
12Recovery of the Acoustical Assumptions. Estimates for Up to the Next to the Top Order Angular Derivatives of χ\chi and Spatial Derivatives of μ\mupp. 665–740
13The Error Estimates Involving the Top Order Spatial Derivatives of the Acoustical Entities. The Energy Estimates. Recovery of the Bootstrap Assumptions. Statement and Proof of the Main Theorem: Existence up to Shock Formationpp. 741–892
14Sufficient Conditions on the Initial Data for the Formation of a Shock in the Evolutionpp. 893–926
15The Nature of the Singular Hypersurface. The Invariant Curves. The Trichotomy Theorem. The Structure of the Boundary of the Domain of the Maximal Solutionpp. 927–975
Epiloguepp. 977–986
Bibliographypp. 987–988
Indexpp. 989–992

Supplementary Material