Large homogeneous initial data for the 3D Navier-Stokes equations
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Mon, 01/02/2010 17:00 |
Pierre-Gilles Lemarié-Rieusset (Université d'Évry) |
Partial Differential Equations Seminar  |
Gibson 1st Floor SR |
| Due to the scaling properties of the Navier-Stokes equations, homogeneous initial data may lead to forward self-similar solutions. When the initial data is small enough, it is well known that the formalism of mild solutions (through the Picard-Duhamel formula) give such self-similar solutions. We shall discuss the issue of large initial data, where we can only prove the existence of weak solutions; those solutions may lack self-similarity, due to the fact that we have no results about uniqueness for such weak solutions. We study some tools which may be useful to get a better understanding of those weak solutions. | |||