关于Boussinesq方程组无粘极限的研究

Research on the Inviscid Limit for Boussinesq Equations

该文主要研究三维Boussinesq方程组的无粘极限问题.为了克服Boussinesq方程组中温度和速度耦合项产生的困难,带温度的涡量方程需要与Slip边界条件匹配,通过计算得到温度更高阶的边界条件,结合迹定理和能量估计,最后得到了三维粘性Boussinesq方程组初边值问题强解的存在唯一性,并在平坦区域上得到了强解的收敛率.

In this paper,we investigate the inviscid limit of the 3D viscous Boussinesq equations with slip boundary condition.We establish the local well-posedness of the strong solutions for initial boundary value problems for such systems.Furthermore,we establish the vanishing viscosity limit process and obtain a strong rate of convergence as the boundary of the domain is flat.In addition,the key observation is that the boundary term asθcan be estimated by the part of high order of energy through the trace formula.