Well-posedness of the linearized Prandtl equation around a non-monotonic shear flow

Dongxiang Chen; Yuxi Wang; Zhifei Zhang

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arXiv · 1609.08785

Well-posedness of the linearized Prandtl equation around a non-monotonic shear flow

Dongxiang Chen·Yuxi Wang·Zhifei Zhang

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Abstract

In this paper, we prove the well-posedness of the linearized Prandtl equation around a non-monotonic shear flow in Gevrey class $2-\theta$ for any $\theta>0$. This result is almost optimal by the ill-posedness result proved by G\'{e}rard-Varet and Dormy, who construct a class of solution with the growth like $e^{\sqrt{k}t}$ for the linearized Prandtl equation around a non-monotonic shear flow.

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Dongxiang Chen, Yuxi Wang, Zhifei Zhang. 2016-09-28. Well-posedness of the linearized Prandtl equation around a non-monotonic shear flow. https://arxiv.org/abs/1609.08785

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