Remarks on the Prandtl Equation

Details Remarks on the Prandtl Equation Remarks on the Prandtl Equation

2011-08-05

arxiv.org/abs/1108.1269v1

Mathematics

Analysis of PDEs

Scientific paper

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 satis?es 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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