On the 3D spherically symmetric free surface problem for full compressible Navier–Stokes equations with outer pressure or surface tension

For the free surface problem of the system of full compressible Navier–Stokes equations in three dimensions with the outer pressure or surface tension and a rigid core in the center, the global existence of strong solutions is proved in this paper. Moreover, when the surface tension vanishes but outer pressure has a lower positive bound, we obtain the uniform estimates independent of time, along with the large-time behavior of solutions under some conditions of the time derivative of the outer pressure, while we obtain the uniform-in-time bounds for the radius of the free surface and density when the outer pressure vanishes, but the surface tension coefficient remains positive. © 2025, International Press, Inc.. All rights reserved.