This paper studies the low Mach number limit of the full compressible Navier-Stokes equations in a three-dimensional bounded domain where the velocity field and the temperature satisfy the slip boundary conditions and the Neumann boundary condition, respectively. The uniform estimates in the Mach number for the strong solutions are derived in a short time interval, provided that the initial density and temperature are close to the constant states and satisfy the "bounded derivative conditions". Thus the solutions of the full compressible Navier-Stokes equations converge to the one of the isentropic incompressible Navier-Stokes equations, as the Mach number vanishes.
Dou, C., Jiang, S., & Ou, Y. (2015). Low Mach number limit of full Navier-Stokes equations in a 3D bounded domain. Journal of Differential Equations, 258(2), 379–398. https://doi.org/10.1016/j.jde.2014.09.017