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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


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


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


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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