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Volume 1, Issue 4
3D Hyperbolic Navier-Stokes Equations in a Thin Strip: Global Well-Posedness and Hydrostatic Limit in Gevrey Space

Wei-Xi Li & Tong Yang

DOI: 10.4208/cmaa.2022-0007

Commun. Math. Anal. Appl., 1 (2022), pp. 471-502.

Published online: 2022-10

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  • Abstract

We consider a hyperbolic version of three-dimensional anisotropic Navier-Stokes equations in a thin strip and its hydrostatic limit that is a hyperbolic Prandtl type equations. We prove the global-in-time existence and uniqueness for the two systems and the hydrostatic limit when the initial data belong to the Gevrey function space with index 2. The proof is based on a direct energy method by observing the damping effect in the systems.

  • Keywords

3D hydrostatic Navier-Stokes equations, global well-posedness, Gevrey class, hydrostatic limit.

  • AMS Subject Headings

35Q30, 76D03, 76D10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMAA-1-471, author = {Li , Wei-Xi and Yang , Tong}, title = {3D Hyperbolic Navier-Stokes Equations in a Thin Strip: Global Well-Posedness and Hydrostatic Limit in Gevrey Space}, journal = {Communications in Mathematical Analysis and Applications}, year = {2022}, volume = {1}, number = {4}, pages = {471--502}, abstract = {

We consider a hyperbolic version of three-dimensional anisotropic Navier-Stokes equations in a thin strip and its hydrostatic limit that is a hyperbolic Prandtl type equations. We prove the global-in-time existence and uniqueness for the two systems and the hydrostatic limit when the initial data belong to the Gevrey function space with index 2. The proof is based on a direct energy method by observing the damping effect in the systems.

}, issn = {2790-1939}, doi = {https://doi.org/10.4208/cmaa.2022-0007}, url = {http://global-sci.org/intro/article_detail/cmaa/21119.html} }
TY - JOUR T1 - 3D Hyperbolic Navier-Stokes Equations in a Thin Strip: Global Well-Posedness and Hydrostatic Limit in Gevrey Space AU - Li , Wei-Xi AU - Yang , Tong JO - Communications in Mathematical Analysis and Applications VL - 4 SP - 471 EP - 502 PY - 2022 DA - 2022/10 SN - 1 DO - http://doi.org/10.4208/cmaa.2022-0007 UR - https://global-sci.org/intro/article_detail/cmaa/21119.html KW - 3D hydrostatic Navier-Stokes equations, global well-posedness, Gevrey class, hydrostatic limit. AB -

We consider a hyperbolic version of three-dimensional anisotropic Navier-Stokes equations in a thin strip and its hydrostatic limit that is a hyperbolic Prandtl type equations. We prove the global-in-time existence and uniqueness for the two systems and the hydrostatic limit when the initial data belong to the Gevrey function space with index 2. The proof is based on a direct energy method by observing the damping effect in the systems.

Li , Wei-Xi and Yang , Tong. (2022). 3D Hyperbolic Navier-Stokes Equations in a Thin Strip: Global Well-Posedness and Hydrostatic Limit in Gevrey Space. Communications in Mathematical Analysis and Applications. 1 (4). 471-502. doi:10.4208/cmaa.2022-0007
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