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arXiv · 2401.11230

Gevrey well-posedness of quasi-linear hyperbolic Prandtl equations

Wei-Xi Li·Tong Yang·Ping Zhang
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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.

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Wei-Xi Li, Tong Yang, Ping Zhang. 2024-01-20. Gevrey well-posedness of quasi-linear hyperbolic Prandtl equations. https://arxiv.org/abs/2401.11230

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