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arXiv · 1706.08120

Ill-posedness of Naiver-Stokes equations and critical Besov-Morrey spaces

Qixiang Yang·Haibo Yang·Huoxiong Wu
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Abstract

The blow up phenomenon in the first step of the classical Picard's scheme was proved in this paper. For certain initial spaces, Bourgain-Pavlovi\'c and Yoneda proved the ill-posedness of the Navier-Stokes equations by showing the norm inflation in certain solution spaces. But Chemin and Gallagher said the space $\dot{B}^{-1,\infty}_{\infty}$ seems to be optimal for some solution spaces best chosen. In this paper, we consider more general initial spaces than Bourgain-Pavlovi\'c and Yoneda did and establish ill-posedness result independent of the choice of solution space. Our result is a complement of the previous ill-posedness results on Navier-Stokes equations.

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Qixiang Yang, Haibo Yang, Huoxiong Wu. 2017-06-25. Ill-posedness of Naiver-Stokes equations and critical Besov-Morrey spaces. https://arxiv.org/abs/1706.08120

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