An Introduction to Navier-Stokes Equation and Oceanography

Introduction.- 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.- References.- Index.