Gevrey well-posedness of quasi-linear hyperbolic Prandtl equations

Wei-Xi Li; Tong Yang; Ping Zhang

Gevrey well-posedness of quasi-linear hyperbolic Prandtl equations

Analysis of PDEs 2024-01-23 v1

Authors: Wei-Xi Li , Tong Yang , Ping Zhang

Abstract

We study the hyperbolic version of the Prandtl system derived from the hyperbolic Navier-Stokes system with no-slip boundary condition. Compared to the classical Prandtl system, the quasi-linear terms in the hyperbolic Prandtl equation leads to an additional instability mechanism. To overcome the loss of derivatives in all directions in the quasi-linear term, we introduce a new auxiliary function for the well-posedness of the system in an anisotropic Gevrey space which is Gevrey class $\frac 32$ in the tangential variable and is analytic in the normal variable.

Keywords

hyperbolic Prandtl equations quasi-linear Gevrey well-posedness anisotropic Gevrey space loss of derivatives boundary layer

Cite

@article{arxiv.2401.11230,
  title  = {Gevrey well-posedness of quasi-linear hyperbolic Prandtl equations},
  author = {Wei-Xi Li and Tong Yang and Ping Zhang},
  journal= {arXiv preprint arXiv:2401.11230},
  year   = {2024}
}

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