Nonlinear stability of non-rotating gaseous stars

For the non-rotating gaseous stars modeled by the compressible Euler–Poisson system with general pressure law, Lin and Zeng (Comm Pure Appl Math 75: 2511–2572, 2022) proved a turning point principle, which gives the sharp linear stability/instability criteria for the non-rotating gaseous stars. In this paper, we prove that the sharp linear stability criterion for the non-rotating stars also implies nonlinear orbital stability against general perturbations provided the global weak solutions exist. If the perturbations are further restricted to be spherically symmetric, then nonlinear stability holds true unconditionally in the sense that the existence of global weak solutions near the non-rotating star can be proved.