Remarks on the Prandtl Equation

Ding Yutao

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arXiv · 1108.1269

Remarks on the Prandtl Equation

Ding Yutao

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Abstract

In a recent result of Gerard-Varet and Dormy [5], they established ill-posedness for the Cauchy problem of the linearized Prandtl equation around non-monotic special solution which is independent of x and satisfies the heat equation. In [6] and [7], some nonlinear ill-posedness were established with this counterexample. Then it is natural to consider the problem that does this linear ill-posedness happen whenever the non-degenerate critical points appear. In this paper, we concern the linearized Prandtl equation around general stationary solutions with non-degenerate critical points depending on x which could be considered as the time-periodic solutions and show some ill-posdness.

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Ding Yutao. 2011-08-05. Remarks on the Prandtl Equation. https://arxiv.org/abs/1108.1269

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