TY - JOUR
T1 - Zero Viscosity-Diffusivity Limit for the Incompressible Boussinesq Equations in Gevrey Class
AU - Cheng , Feng
JO - Communications in Mathematical Research 
VL - 4
SP - 579
EP - 604
PY - 2022
DA - 2022/10
SN - 38
DO - http://doi.org/10.4208/cmr.2021-0075
UR - https://global-sci.org/intro/article_detail/cmr/21073.html
KW - Gevrey class, incompressible Boussinesq equation, analyticity, zero viscosity-diffusivity limit, convergence rate.
AB - <p style="text-align: justify;">In this paper, we study the zero viscosity-diffusivity limit for the
incompressible Boussinesq equations in a periodic domain in the framework of
Gevrey class. We first prove that there exists an interval of time, independent of
the viscosity coefficient and the diffusivity coefficient, for the solutions to the
viscous incompressible Boussinesq equations. Then, based on these uniform
estimates, we show that the solutions of the viscous incompressible Boussinesq
equations converge to that of the ideal incompressible Boussinesq equations as
the viscosity and diffusivity coefficients go to zero. Moreover, the convergence
rate is also given.</p>