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Volume 2, Issue 4
Gevrey Well-Posedness of Quasi-Linear Hyperbolic Prandtl Equations

Wei-Xi Li, Tong Yang & Ping Zhang

DOI: 10.4208/cmaa.2023-0007

Commun. Math. Anal. Appl., 2 (2023), pp. 388-420.

Published online: 2023-11

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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 3/2 in the tangential variable and is analytic in the normal variable.

  • Keywords

Hyperbolic Prandtl equations, quasi-linear, Gevrey class.

  • AMS Subject Headings

76D10, 76D03, 35L80, 35L72, 35Q30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMAA-2-388, author = {Li , Wei-XiYang , Tong and Zhang , Ping}, title = {Gevrey Well-Posedness of Quasi-Linear Hyperbolic Prandtl Equations}, journal = {Communications in Mathematical Analysis and Applications}, year = {2023}, volume = {2}, number = {4}, pages = {388--420}, 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 3/2 in the tangential variable and is analytic in the normal variable.

}, issn = {2790-1939}, doi = {https://doi.org/10.4208/cmaa.2023-0007}, url = {http://global-sci.org/intro/article_detail/cmaa/22148.html} }
TY - JOUR T1 - Gevrey Well-Posedness of Quasi-Linear Hyperbolic Prandtl Equations AU - Li , Wei-Xi AU - Yang , Tong AU - Zhang , Ping JO - Communications in Mathematical Analysis and Applications VL - 4 SP - 388 EP - 420 PY - 2023 DA - 2023/11 SN - 2 DO - http://doi.org/10.4208/cmaa.2023-0007 UR - https://global-sci.org/intro/article_detail/cmaa/22148.html KW - Hyperbolic Prandtl equations, quasi-linear, Gevrey class. AB -

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 3/2 in the tangential variable and is analytic in the normal variable.

Wei-Xi Li, Tong Yang & Ping Zhang. (2023). Gevrey Well-Posedness of Quasi-Linear Hyperbolic Prandtl Equations. Communications in Mathematical Analysis and Applications. 2 (4). 388-420. doi:10.4208/cmaa.2023-0007
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