An Introduction to Navier'Stokes Equation and Oceanography

1. Basic physical laws and units

2. Radiation balance of atmosphere

3. Conservations in ocean and atmosphere

4. Sobolev spaces I

5. Particles and continuum mechanics

6. Conservation of mass and momentum

7. Conservation of energy

8. One-dimensional wave equation

9. Nonlinear effects, shocks

10. Sobolev spaces II

11. Linearized elasticity

12. Ellipticity conditions

13. Sobolev spaces III

14. Sobolev spaces IV

15. Sobolev spaces V

16. Sobolev embedding theorem

17. Fixed point theorems

18. Brouwer's topological degree

19. Time-dependent solutions I

20. Time-dependent solutions II

21. Time-dependent solutions III

22. Uniqueness in 2 dimensions

23. Traces

24. Using compactness

25. Existence of smooth solutions

26. Semilinear models

27. Size of singular sets

28. Local estimates, compensated integrability

29. Coriolis force

30. Equation for the vorticity

31. Boundary conditions in linearized elasticity

32. Turbulence, homogenization

33. G-convergence and H-convergence

34. One-dimensional homogenization, Young measures

35. Nonlocal effects I

36. Nonlocal effects II

37. A model problem

38. Compensated compactness I

39. Compensated compactness II

40. Differential forms

41. The compensated compactness method

42. H-measures and variants

43. Biographical Information

44. Abbreviations and Mathematical Notation

DRM-restrictions

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Keywords: MATHEMATICS / General MAT000000