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 - <p style="text-align: justify;">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.</p>