The Formation of Shocks in 3-Dimensional Fluids

Demetrios Christodoulou

doi:10.4171/031

BooksemmMonograph

The Formation of Shocks in 3-Dimensional Fluids

Demetrios Christodoulou
ETH Zürich, Switzerland

Buy from €159.00Download PDF

A subscription is required to access this book.

	FrontmatterDownload pp. i–v
	ContentsDownload pp. vii–viii
	Prologue and SummaryDownload pp. 1–21
1	Relativistic Fluids and Nonlinear Wave Equations. The Equations of Variationpp. 23–37
2	The Basic Geometric Constructionpp. 39–52
3	The Acoustical Structure Equationspp. 53–83
4	The Acoustical Curvaturepp. 85–98
5	The Fundamental Energy Estimatepp. 99–137
6	Construction of the Commutation Vectorfieldspp. 139–168
7	Outline of the Derived Estimates of Each Orderpp. 169–201
8	Regularization of the Propagation Equation for $d$ tr $χ$ . Estimates for the Top Order Angular Derivatives of $χ$ pp. 203–273
9	Regularization of the Propagation Equation for $Δ μ$ . Estimates for the Top Order Spatial Derivatives of $μ$ pp. 275–328
10	Control of the Angular Derivatives of the First Derivatives of the $x^{i}$ . Assumptions and Estimates in Regard to $χ$ pp. 329–472
11	Control of the Spatial Derivatives of the First Derivatives of the $x^{i}$ . Assumptions and Estimates in Regard to $μ$ pp. 473–664
12	Recovery of the Acoustical Assumptions. Estimates for Up to the Next to the Top Order Angular Derivatives of $χ$ and Spatial Derivatives of $μ$ pp. 665–740
13	The 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
14	Sufficient Conditions on the Initial Data for the Formation of a Shock in the Evolutionpp. 893–926
15	The 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