An Introduction to Navier-Stokes Equation and Oceanography
The Introduction to Navier-Stokes Equation and Oceanography corresponds to a graduate course in mathematics, taught at Carnegie Mellon University in the spring of 1999. Comments were added to the lecture notes distributed to the students, as well as short biographical information for all scientists...
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| Format: | eBook |
| Language: | English |
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Berlin, Heidelberg
Springer Berlin Heidelberg
2006, 2006
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| Edition: | 1st ed. 2006 |
| Series: | Lecture Notes of the Unione Matematica Italiana
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| Subjects: | |
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| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Table of Contents:
- Basic physical laws and units
- Radiation balance of atmosphere
- Conservations in ocean and atmosphere
- Sobolev spaces I
- Particles and continuum mechanics
- Conservation of mass and momentum
- Conservation of energy
- One-dimensional wave equation
- Nonlinear effects, shocks
- Sobolev spaces II
- Linearized elasticity
- Ellipticity conditions
- Sobolev spaces III
- Sobolev spaces IV
- Sobolev spaces V
- Sobolev embedding theorem
- Fixed point theorems
- Brouwer's topological degree
- Time-dependent solutions I
- Time-dependent solutions II
- Time-dependent solutions III
- Uniqueness in 2 dimensions
- Traces
- Using compactness
- Existence of smooth solutions
- Semilinear models
- Size of singular sets
- Local estimates, compensated integrability
- Coriolis force
- Equation for the vorticity
- Boundary conditions in linearized elasticity
- Turbulence, homogenization
- G-convergence and H-convergence
- One-dimensional homogenization, Young measures
- Nonlocal effects I
- Nonlocal effects II
- A model problem
- Compensated compactness I
- Compensated compactness II
- Differential forms
- The compensated compactness method
- H-measures and variants
- Biographical Information
- Abbreviations and Mathematical Notation