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Pré-Publication, Document De Travail Année : 2015

Gevrey class smoothing effect for the Prandtl equation

Résumé

It is well known that the Prandtl boundary layer equation is instable, and the well-posedness in Sobolev space for the Cauchy problem is an open problem. Recently, under the Oleinik's monotonicity assumption for the initial datum, [1] have proved the local well-posedness of Cauchy problem in Sobolev space (see also [21]). In this work, we study the Gevrey smoothing effects of the local solution obtained in [1]. We prove that the Sobolev's class solution belongs to some Gevrey class with respect to tangential variables at any positive time.
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Dates et versions

hal-01115829 , version 1 (11-02-2015)
hal-01115829 , version 2 (06-04-2015)
hal-01115829 , version 3 (15-05-2015)

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Weixi Li, Di Wu, Chao-Jiang Xu. Gevrey class smoothing effect for the Prandtl equation. 2015. ⟨hal-01115829v3⟩
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