INCOMPRESSIBLE LIMIT OF ISENTROPIC NAVIER—STOKES EQUATIONS WITH ILL-PREPARED DATA IN BOUNDED DOMAINS.

In this paper, we study the incompressible limit of strong solutions to the isentropic compressible Navier—Stokes equations with ill-prepared initial data and slip boundary condition in a three-dimensional bounded domain. Previous results only deal with the cases of the weak solutions or the cases without solid boundary, where the uniform estimates are much easier to be shown. We propose a new weighted energy functional to establish the uniform estimates, in particular for the time derivatives and the high-order spatial derivatives. The estimates of highest-order spatial derivatives of fast variables are subtle and crucial for the uniform bounds of solutions. The incompressible limit is shown by applying the Helmholtz decomposition, the weak convergence of the velocity, and the strong convergence of its divergence-free component. [ABSTRACT FROM AUTHOR]