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Other Models: Uniqueness and Singularities

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Part of the Lecture Notes in Mathematics book series (LNMECOLE,volume 2015)

Abstract

This chapter contains a number of other examples, presented for different purposes. Not only the uniqueness problem but also emergence of singularities is discussed. First, we give a few examples where noise does not change the difficulties related to these two issues; a little bit improperly, we call them “negative” examples (in spite of the fact that they are very interesting). Then we show two examples where singularities are prevented by noise: continuity equation and vortex point motion. We call them “positive” examples. The next section on nonlinear Schrödinger equation describes theoretical and numerical results both of positive and negative type. Finally, we summarize the attempts made on the 3D stochastic Navier–Stokes equations, in the direction of understanding uniqueness and singularities.

Keywords

  • Euler Equation
  • Additive Noise
  • Multiplicative Noise
  • Point Vortex
  • Deterministic Case

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Correspondence to Franco Flandoli .

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© 2011 Springer-Verlag Berlin Heidelberg

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Flandoli, F. (2011). Other Models: Uniqueness and Singularities. In: Random Perturbation of PDEs and Fluid Dynamic Models. Lecture Notes in Mathematics(), vol 2015. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18231-0_5

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