An Introduction to Navier'Stokes Equation and Oceanography

Basic physical laws and units....Pages 1-5
Radiation balance of atmosphere....Pages 7-10
Conservations in ocean and atmosphere....Pages 11-14
Sobolev spaces I....Pages 15-22
Particles and continuum mechanics....Pages 23-30
Conservation of mass and momentum....Pages 31-36
Conservation of energy....Pages 37-41
One-dimensional wave equation....Pages 43-48
Nonlinear effects, shocks....Pages 49-56
Sobolev spaces II....Pages 57-62
Linearized elasticity....Pages 63-67
Ellipticity conditions....Pages 69-72
Sobolev spaces III....Pages 73-76
Sobolev spaces IV....Pages 77-81
Sobolev spaces V....Pages 83-86
Sobolev embedding theorem....Pages 87-93
Fixed point theorems....Pages 95-100
Brouwer\'s topological degree....Pages 101-105
Time-dependent solutions I....Pages 107-112
Time-dependent solutions II....Pages 113-117
Time-dependent solutions III....Pages 119-124
Uniqueness in 2 dimensions....Pages 125-127
Traces....Pages 129-135
Using compactness....Pages 137-141
Existence of smooth solutions....Pages 143-146
Semilinear models....Pages 147-154
Size of singular sets....Pages 155-159
Local estimates, compensated integrability....Pages 161-165
Coriolis force....Pages 167-169
Equation for the vorticity....Pages 171-172
Boundary conditions in linearized elasticity....Pages 173-176
Turbulence, homogenization....Pages 177-180
G-convergence and H-convergence....Pages 181-185
One-dimensional homogenization, Young measures....Pages 187-190
Nonlocal effects I....Pages 191-195
Nonlocal effects II....Pages 197-200
A model problem....Pages 201-204
Compensated compactness I....Pages 205-208
Compensated compactness II....Pages 209-211
Differential forms....Pages 213-217
The compensated compactness method....Pages 219-224
H-measures and variants....Pages 225-232
Biographical Information....Pages 233-236
Abbreviations and Mathematical Notation....Pages 237-240