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## Relativistic Fluids

*Yvonne Choquet-Bruhat*

### in General Relativity and the Einstein Equations

- Published in print:
- 2008
- Published Online:
- May 2009
- ISBN:
- 9780199230723
- eISBN:
- 9780191710872
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199230723.003.0009
- Subject:
- Mathematics, Applied Mathematics

This chapter presents general properties of perfect fluids. When appropriate definitions are given, some of these properties generalize well-known properties of non-relativistic perfect fluids. ... More

## Other Hyperbolic-Elliptic Well-Posed Systems

*Yvonne Choquet-Bruhat*

### in General Relativity and the Einstein Equations

- Published in print:
- 2008
- Published Online:
- May 2009
- ISBN:
- 9780199230723
- eISBN:
- 9780191710872
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199230723.003.0008
- Subject:
- Mathematics, Applied Mathematics

This chapter presents well-posed hyperbolic or hyperbolic-elliptic systems that lead to the same local existence andgeometric uniqueness theorems as the wave gauge choice. However, these different ... More

## Problems in nonlinear electromagnetism

*Mauro Fabrizio and Morro Angelo*

### in Electromagnetism of Continuous Media: Mathematical Modelling and Applications

- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198527008
- eISBN:
- 9780191713316
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198527008.003.0010
- Subject:
- Mathematics, Applied Mathematics

This chapter presents some nonlinear constitutive models and develops wave propagation problems in nonlinear electromagnetism. Nonlinear models arise from nonlinear functions or functionals, which ... More

## Relativistic Hydrodynamics

*Luciano Rezzolla and Olindo Zanotti*

- Published in print:
- 2013
- Published Online:
- January 2014
- ISBN:
- 9780198528906
- eISBN:
- 9780191746505
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528906.001.0001
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

The book provides a lively and approachable introduction to the main concepts and techniques of relativistic hydrodynamics in a form which will appeal to physicists at advanced undergraduate and ... More

## On the Bounded L2 Curvature Conjecture

*Sergiu Klainerman*

*Charles Fefferman, Alexandru D. Ionescu, D. H. Phong, and Stephen Wainger (eds)*

### in Advances in Analysis: The Legacy of Elias M. Stein

- Published in print:
- 2014
- Published Online:
- October 2017
- ISBN:
- 9780691159416
- eISBN:
- 9781400848935
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691159416.003.0010
- Subject:
- Mathematics, Numerical Analysis

This chapter deals with a fundamental application of new methods to a geometric quasilinear equation to settle an important conjecture in General Relativity. According to the bounded L² curvature ... More

## Rotating Shallow-Water Models as Quasilinear Hyperbolic Systems, and Related Numerical Methods

*Vladimir Zeitlin*

### in Geophysical Fluid Dynamics: Understanding (almost) everything with rotating shallow water models

- Published in print:
- 2018
- Published Online:
- April 2018
- ISBN:
- 9780198804338
- eISBN:
- 9780191842627
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198804338.003.0007
- Subject:
- Physics, Geophysics, Atmospheric and Environmental Physics

The chapter contains the mathematical background necessary to understand the properties of RSW models and numerical methods for their simulations. Mathematics of RSW model is presented by using their ... More

## The Finite-Volume Method

*Heiner Igel*

### in Computational Seismology: A Practical Introduction

- Published in print:
- 2016
- Published Online:
- January 2017
- ISBN:
- 9780198717409
- eISBN:
- 9780191835070
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198717409.003.0008
- Subject:
- Physics, Geophysics, Atmospheric and Environmental Physics

The finite-volume method is introduced as a consequence of a general (mass, tracer, energy) conservation problem. The wave equation is derived from this fundamental conservation principle. The ... More

## Waves in a Discrete World

*Heiner Igel*

### in Computational Seismology: A Practical Introduction

- Published in print:
- 2016
- Published Online:
- January 2017
- ISBN:
- 9780198717409
- eISBN:
- 9780191835070
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198717409.003.0003
- Subject:
- Physics, Geophysics, Atmospheric and Environmental Physics

The general classification of partial differential equations is described, and fundamental concepts to discretize seismic wavefields are introduced. The consequences of the problem dimensionality ... More

## The Discontinuous Galerkin Method

*Heiner Igel*

### in Computational Seismology: A Practical Introduction

- Published in print:
- 2016
- Published Online:
- January 2017
- ISBN:
- 9780198717409
- eISBN:
- 9780191835070
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198717409.003.0009
- Subject:
- Physics, Geophysics, Atmospheric and Environmental Physics

The discontinuous Galerkin method is introduced as a special type of finite-element method in which the solution fields are allowed to be discontinuous at the element boundaries. This requires the ... More

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