members:lemarie:ns21toc
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members:lemarie:ns21toc [2016/03/23 19:26] Pierre Gilles Lemarié [History of the equation] |
members:lemarie:ns21toc [2016/03/23 19:28] Pierre Gilles Lemarié [Mild solutions in Lebesgue or Sobolev spaces] |
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| ===== Classical solutions ===== | ===== Classical solutions ===== | ||
| - | The heat kernel | + | |
| - | The Poisson equation | + | * The heat kernel |
| - | The Helmholtz decomposition | + | * The Poisson equation |
| - | The Stokes equation | + | * The Helmholtz decomposition |
| - | The Oseen tensor | + | * The Stokes equation |
| - | Classical solutions for the Navier–Stokes problem | + | * The Oseen tensor |
| - | Small data and global solutions | + | * Classical solutions for the Navier–Stokes problem |
| - | Time asymptotics for global solutions | + | * Small data and global solutions |
| - | Steady solutions | + | * Time asymptotics for global solutions |
| - | Spatial asymptotics | + | * Steady solutions |
| - | Spatial asymptotics for the vorticity | + | * Spatial asymptotics |
| - | Intermediate conclusion | + | * Spatial asymptotics for the vorticity |
| + | * Intermediate conclusion | ||
| ===== A capacitary approach of the Navier–Stokes integral equations ===== | ===== A capacitary approach of the Navier–Stokes integral equations ===== | ||
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| ===== Mild solutions in Lebesgue or Sobolev spaces ===== | ===== Mild solutions in Lebesgue or Sobolev spaces ===== | ||
| - | Kato's mild solutions | + | |
| - | Local solutions in the Hilbertian setting | + | * Kato's mild solutions |
| - | Global solutions in the Hilbertian setting | + | * Local solutions in the Hilbertian setting |
| - | Sobolev spaces | + | * Global solutions in the Hilbertian setting |
| - | A commutator estimate | + | * Sobolev spaces |
| - | Lebesgue spaces | + | * A commutator estimate |
| - | Maximal functions | + | * Lebesgue spaces |
| - | Basic lemmas on real interpolation spaces | + | * Maximal functions |
| - | Uniqueness of L3 solutions | + | * Basic lemmas on real interpolation spaces |
| + | * Uniqueness of L^3 solutions | ||
| ===== Mild solutions in Besov or Morrey spaces ===== | ===== Mild solutions in Besov or Morrey spaces ===== | ||
members/lemarie/ns21toc.txt · Last modified: 2016/03/23 19:30 by Pierre Gilles Lemarié
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