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On nonlinear instability of liquid Lane-Emden stars
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math.AP
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liquidinstabilitylane-emdennonlinearstarsadiabaticanalysisboundary
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abstract
We establish a dynamical nonlinear instability of liquid Lane-Emden stars in $\mathbb{R}^{3}$ whose adiabatic exponents take values in $[1,\frac43)$. Our proof relies on a priori estimates for the free boundary problem of a compressible self-gravitating liquid, as well as a quantitative analysis of the competition between the fastest linear growing mode and the source.
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