Mathematical Theory of Compressible Viscous Fluids

1. Preliminaries, Notation, and Spaces of Functions
Eduard Feireisl, Trygve G. Karper, Milan Pokorný

Part I. Mathematics of Compressible Fluid Flows

2. Mathematical Model
Eduard Feireisl, Trygve G. Karper, Milan Pokorný

3. Weak Solutions
Eduard Feireisl, Trygve G. Karper, Milan Pokorný

4. A Priori Bounds
Eduard Feireisl, Trygve G. Karper, Milan Pokorný

5. Weak Formulation Revisited
Eduard Feireisl, Trygve G. Karper, Milan Pokorný

6. Weak Sequential Stability
Eduard Feireisl, Trygve G. Karper, Milan Pokorný

Part II. Existence of Weak Solutions via a Numerical Method

7. Numerical Method
Eduard Feireisl, Trygve G. Karper, Milan Pokorný

8. Stability of the Numerical Method
Eduard Feireisl, Trygve G. Karper, Milan Pokorný

9. Consistency
Eduard Feireisl, Trygve G. Karper, Milan Pokorný

10. Convergence
Eduard Feireisl, Trygve G. Karper, Milan Pokorný

Part III. Existence Theory for General Pressure

11. Weak Solutions with Artificial Pressure
Eduard Feireisl, Trygve G. Karper, Milan Pokorný

12. Strong Convergence of the Approximate Densities
Eduard Feireisl, Trygve G. Karper, Milan Pokorný

13. Concluding Remarks and Suggestions forFurther Reading
Eduard Feireisl, Trygve G. Karper, Milan Pokorný

Keywords: Mathematics, Partial Differential Equations, Numerical Analysis, Mathematical Methods in Physics, Fourier Analysis, Functional Analysis, Mathematical Applications in the Physical Sciences