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arXiv · 2504.17136

Global stability for compressible isentropic Navier-Stokes equations in 3D bounded domains with Navier-slip boundary conditions

Yang Liu·Guochun Wu·Xin Zhong
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Abstract

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.

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Yang Liu, Guochun Wu, Xin Zhong. 2025-10-16. Global stability for compressible isentropic Navier-Stokes equations in 3D bounded domains with Navier-slip boundary conditions. https://doi.org/10.1007/s00332-026-10294-4

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