We investigate the global stability of large solutions to the compressible
isentropic Navier-Stokes equations in a three-dimensional (3D) bounded domain
with Navier-slip boundary conditions. It is shown that the strong solutions
converge to an equilibrium state exponentially in the $L^2$-norm provided the
density is essentially uniform-in-time bounded from above. Moreover, we obtain
that the density converges to its equilibrium state exponentially in the
$L^\infty$-norm if additionally the initial density is bounded away from zero.
Furthermore, we derive that the vacuum states will not vanish for any time
provided vacuum appears (even at a point) initially. This is the first result
concerning the global stability for large strong solutions of compressible
Navier-Stokes equations with vacuum in 3D general bounded domains.

Cet article explore les excursions dans le temps et leurs implications.

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